QUESTION 167
A sphere has a radius of 3 cm. Its volume, in cubic centimeters, is
(A) $12\pi$
(B) $18\pi$
(C) $24\pi$
(D) $36\pi$
(E) $48\pi$

QUESTION 171
The perimeter of an equilateral triangle with side 8 cm is
(A) 16 cm
(B) 20 cm
(C) 24 cm
(D) 28 cm
(E) 32 cm

QUESTION 174
The area of a trapezoid with parallel bases of 6 cm and 10 cm and height 4 cm is
(A) 24 cm$^2$
(B) 28 cm$^2$
(C) 32 cm$^2$
(D) 36 cm$^2$
(E) 40 cm$^2$

QUESTION 177
The value of $\frac{3}{4} + \frac{5}{6}$ is
(A) $\frac{8}{10}$
(B) $\frac{19}{12}$
(C) $\frac{4}{5}$
(D) $\frac{7}{6}$
(E) $\frac{8}{12}$

A lapidary received from a jeweler the commission to work on a precious stone whose shape is that of a pyramid, as illustrated in Figure 1. To do so, the lapidary will make four cuts of equal formats at the corners of the base. The removed corners correspond to small pyramids, at the vertices $P, Q, R$ and $S$, along the dashed segments, illustrated in Figure 2.
After making the cuts, the lapidary obtained, from the larger stone, a polyhedral jewel whose numbers of faces, edges and vertices are, respectively, equal to
(A) 9, 20 and 13.
(B) 9, 24 and 13.
(C) 7, 15 and 12.
(D) 10, 16 and 5.
(E) 11, 16 and 5.

Brazil is the fourth largest food producer in the world and is also one of the world champions in food waste. Approximately 150 million tons of food are produced per year, and of that total, $\frac{2}{3}$ are planting products. In relation to what is planted, 64\% are lost along the production chain (20\% lost in harvesting, 8\% in transport and storage, 15\% in processing industry, 1\% in retail and the remainder in culinary processing and eating habits).
The waste during culinary processing and eating habits, in million tons, is equal to
(A) 20.
(B) 30.
(C) 56.
(D) 64.
(E) 96.

The fastest land vehicle ever manufactured to date is the Sonic Wind LSRV, which is being prepared to reach a speed of $3000 \mathrm{~km}/\mathrm{h}$. It is faster than the Concorde, one of the fastest passenger aircraft ever made, which reaches $2330 \mathrm{~km}/\mathrm{h}$.
For a fixed distance, speed and time are inversely proportional.
To cover a distance of 1000 km, the value closest to the difference, in minutes, between the times spent by the Sonic Wind LSRV and the Concorde, at their maximum speeds, is
(A) 0.1.
(B) 0.7.
(C) 6.0.
(D) 11.2.
(E) 40.2.

A farmer lives from growing strawberries that are sold to a cooperative. The cooperative makes a purchase and sale contract in which the producer reports the planted area.
To allow proper plant growth, strawberry seedlings are planted in the center of a rectangular area, 10 cm by 20 cm, as shown in the figure.
Currently, his strawberry plantation occupies an area of $10000 \mathrm{~m}^{2}$, but the cooperative wants him to increase his production. For this, the farmer must increase the planted area by 20\%, maintaining the same planting pattern.
The increase (in units) in the number of strawberry seedlings in his plantation should be
(A) 10000.
(B) 60000.
(C) 100000.
(D) 500000.
(E) 600000.

A perfume industry currently packages its products in spherical bottles with radius $R$, with volume given by $\frac{4}{3}\pi \cdot (R)^{3}$.
It was observed that there will be a cost reduction if cylindrical bottles are used with base radius $\frac{R}{3}$, whose volume will be given by $\pi\left(\frac{R}{3}\right)^{2} \cdot h$, where $h$ is the height of the new packaging.
For the same capacity of the spherical bottle to be maintained, the height of the cylindrical bottle (in terms of $R$) should be equal to
(A) $2R$.
(B) $4R$.
(C) $6R$.
(D) $9R$.
(E) $12R$.

A European company built a solar airplane, as shown in the figure, aiming to go around the world using only solar energy. The solar airplane has length $AB$ equal to 20 m and a wing span $CD$ equal to 60 m.
For a science fair, a team of students made a scale model of this airplane. The scale used by the students was $3 : 400$.
The wing span $CD$ in the said model, in centimeters, is equal to
(A) 5.
(B) 20.
(C) 45.
(D) 55.
(E) 80.

The table presents the ranking of the six leading countries on a day of competition at the Olympics. The ranking is done according to the quantities of gold, silver, and bronze medals, respectively.

Country	Gold	Silver	Bronze	Total
$1^{\text{st}}$ China	9	5	3	17
$2^{\text{nd}}$ USA	5	7	4	16
$3^{\text{rd}}$ France	3	1	3	7
$4^{\text{th}}$ Argentina	3	2	2	7
$5^{\text{th}}$ Italy	2	6	2	10
$6^{\text{th}}$ Brazil	2	5	3	10

If the medals obtained by Brazil and Argentina were combined to form a single hypothetical country, what position would that country occupy?
(A) $1^{\text{st}}$
(B) $2^{\text{nd}}$
(C) $3^{\text{rd}}$
(D) $4^{\text{th}}$
(E) $5^{\text{th}}$

A company specializing in pool maintenance uses a water treatment product whose technical specifications suggest adding $1.5 \mathrm{~mL}$ of this product for every 1000 L of pool water. This company was hired to care for a pool with a rectangular base, constant depth equal to $1.7 \mathrm{~m}$, with width and length equal to 3 m and 5 m, respectively. The water level of this pool is maintained at 50 cm from the edge of the pool.
The amount of this product, in milliliters, that should be added to this pool in order to meet its technical specifications is
(A) 11.25.
(B) 27.00.
(C) 28.80.
(D) 32.25.
(E) 49.50.

In a tourist cable car, cabins leave stations at sea level and at the top of a mountain. The crossing takes 1.5 minutes and both cabins move at the same speed. Forty seconds after cabin $A$ departs from the station at sea level, it crosses with cabin $B$, which had left from the top of the mountain.
How many seconds after cabin $B$ departed did cabin $A$ depart?
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25

On a stormy day, the change in the depth of a river, at a certain location, was recorded during a 4-hour period. The results are indicated in the line graph. In it, the depth $h$, recorded at 13 hours, was not noted and, from $h$, each unit on the vertical axis represents one meter.
It was reported that between 15 hours and 16 hours, the depth of the river decreased by 10\%. At 16 hours, what is the depth of the river, in meters, at the location where the records were made?
(A) 18
(B) 20
(C) 24
(D) 36
(E) 40

A hotel chain has simple cabins on the island of Gotland, in Sweden. The support structure of each of these cabins is represented in Figure 2.
The geometric form of the surface whose edges are represented in Figure 2 is
(A) tetrahedron.
(B) rectangular pyramid.
(C) truncated rectangular pyramid.
(D) right rectangular prism.
(E) right triangular prism.

The image presented in the figure is a black and white copy of the square canvas titled The Fish, by Marcos Pinto, which was placed on a wall for exhibition and fixed at points $A$ and $B$. Due to a problem with the fixing of one of the points, the screen came loose, rotating flush against the wall. After the rotation, it was positioned as illustrated in the figure, forming an angle of $45^{\circ}$ with the horizon line.
To reposition the screen in its original position, it must be rotated, flush against the wall, at the smallest possible angle less than $360^{\circ}$. The way to reposition the screen in the original position, following what was established, is by rotating it at an angle of
(A) $90^{\circ}$ clockwise.
(B) $135^{\circ}$ clockwise.
(C) $180^{\circ}$ counterclockwise.
(D) $270^{\circ}$ counterclockwise.
(E) $315^{\circ}$ clockwise.

Water for supplying a building is stored in a system formed by two identical reservoirs, in the shape of a rectangular block, connected to each other by a pipe equal to the inlet pipe. Water enters the system through the inlet pipe in Reservoir 1 at a constant flow rate and, upon reaching the level of the connecting pipe, begins to supply Reservoir 2. Assume that initially both reservoirs are empty. Which of the graphs best describes the height $h$ of the water level in Reservoir 1, as a function of the volume $V$ of water in the system?
(A) [Graph A]
(B) [Graph B]
(C) [Graph C]
(D) [Graph D]
(E) [Graph E]

Consider that the external radius of each pipe in the image is 0.60 m and that they are on top of a truck bed whose upper part is at $1.30 \mathrm{~m}$ from the ground. The drawing represents the rear view of the pipe stacking.
The recommended safety margin for a vehicle to pass under an overpass is that the total height of the vehicle with the load be at least $0.50 \mathrm{~m}$ less than the height of the overpass span.
Consider 1.7 as an approximation for $\sqrt{3}$. What should be the minimum height of the overpass, in meters, for this truck to pass safely under its span?
(A) 2.82
(B) 3.52
(C) 3.70
(D) 4.02
(E) 4.20

A boy has just moved to a new neighborhood and wants to go to the bakery. He asked a friend for help who gave him a map with numbered points, representing five places of interest, among which is the bakery. Furthermore, the friend gave the following instructions: starting from the point where you are, represented by the letter $X$, walk west, turn right at the first street you find, continue straight ahead and turn left at the next street. The bakery will be right after.
The bakery is represented by the numbered point
(A) 1.
(B) 2.
(C) 3.
(D) 4.
(E) 5.

A designer draftsperson must draw a pan lid in circular form. To perform this drawing, she has, at the moment, only a compass whose leg length is 10 cm, a protractor, and a sheet of paper with a Cartesian plane. To sketch this lid, she separated the compass legs so that the angle formed by them was $120^{\circ}$. The needle point is represented by point $C$, the pencil point is represented by point $B$, and the compass head is represented by point $A$.
After completing the drawing, she sends it to the production department. Upon receiving the drawing with the indication of the lid's radius, they will verify in which interval it falls and decide the type of material to be used in its manufacture, according to the data.

Type of material	Interval of radius values (cm)
I	$0 < \mathrm{R} \leq 5$
II	$5 < \mathrm{R} \leq 10$
III	$10 < \mathrm{R} \leq 15$
IV	$15 < \mathrm{R} \leq 21$
V	$21 < \mathrm{R} \leq 40$

Consider 1.7 as an approximation for $\sqrt{3}$. The type of material to be used by the production department will be
(A) I.
(B) II.
(C) III.
(D) IV.
(E) V.

A person received a bracelet made of spherical pearls, in which one of the pearls was missing. She took the jewelry to a jeweler who verified that the diameter measurement of these pearls was 4 millimeters. In his inventory, pearls of the same type and format, available for replacement, had diameters equal to: $4.025 \mathrm{~mm}$; $4.100 \mathrm{~mm}$; $3.970 \mathrm{~mm}$; $4.080 \mathrm{~mm}$ and $3.099 \mathrm{~mm}$.
The jeweler then placed on the bracelet the pearl whose diameter was closest to the diameter of the original pearls.
The pearl placed on the bracelet by the jeweler has a diameter, in millimeters, equal to
(A) 3.099.
(B) 3.970.
(C) 4.025.
(D) 4.080.
(E) 4.100.

On one of his trips, a tourist bought a souvenir of one of the monuments he visited. On the base of the object there is information stating that it is a piece on a scale of 1 : 400, and that its volume is $25 \mathrm{~cm}^{3}$.
The volume of the original monument, in cubic meters, is
(A) 100.
(B) 400.
(C) 1600.
(D) 6250.
(E) 10000.

A mountain bike type bicycle has a chainring with 3 gears and a cassette with 6 gears, which, combined with each other, determine 18 speeds (number of chainring gears times the number of cassette gears).
The number of teeth of the gears on the chainrings and cassettes of this bicycle are listed in the table.

Gears	$\mathbf{1}^{\mathrm{st}}$	$\mathbf{2}^{\mathrm{nd}}$	$\mathbf{3}^{\mathrm{rd}}$	$\mathbf{4}^{\mathrm{th}}$	$\mathbf{5}^{\mathrm{th}}$	$\mathbf{6}^{\mathrm{th}}$
\begin{tabular}{ c } Number of teeth on
chainring

& 46 & 36 & 26 & - & - & - \hline

Number of teeth on

cassette

& 24 & 22 & 20 & 18 & 16 & 14 \hline \end{tabular}
It is known that the number of rotations made by the rear wheel with each pedal stroke is calculated by dividing the number of teeth on the chainring by the number of teeth on the cassette.
During a ride on a bicycle of this type, one wishes to make a route as slowly as possible, choosing for this one of the following gear combinations (chainring x cassette):

$\mathbf{I}$	II	III	IV	V
$1^{\mathrm{st}} \times 1^{\mathrm{st}}$	$1^{\mathrm{st}} \times 6^{\mathrm{th}}$	$2^{\mathrm{nd}} \times 4^{\mathrm{th}}$	$3^{\mathrm{rd}} \times 1^{\mathrm{st}}$	$3^{\mathrm{rd}} \times 6^{\mathrm{th}}$

The combination chosen to perform this ride in the desired way is
(A) I.
(B) II.
(C) III.
(D) IV.
(E) V.

The organizing committee of the 2014 World Cup created the World Cup logo, composed of a flat figure and the slogan ``Together in one rhythm'', with hands that unite forming the FIFA trophy. Consider that the organizing committee decided to use all the colors of the national flag (green, yellow, blue, and white) to color the logo, so that neighboring regions have different colors.
In how many different ways could the World Cup organizing committee paint the logo with the mentioned colors?
(A) 15
(B) 30
(C) 108
(D) 360
(E) 972

In a park there are two viewpoints of different heights that are accessed by a panoramic elevator. The top of viewpoint 1 is accessed by elevator 1, while the top of viewpoint 2 is accessed by elevator 2. They are at a distance that can be traveled on foot, and between the viewpoints there is a cable car that connects them which may or may not be used by the visitor.
Access to the elevators has the following costs:

• Going up by elevator 1: $\mathrm{R}\$ 0.15$;
• Going up by elevator 2: $\mathrm{R}\$ 1.80$;
• Going down by elevator 1: $\mathrm{R}\$ 0.10$;
• Going down by elevator 2: $\mathrm{R}\$ 2.30$.

The cost of the cable car ticket departing from the top of viewpoint 1 to the top of viewpoint 2 is $\mathrm{R}\$ 2.00$, and from the top of viewpoint 2 to the top of viewpoint 1 is $\mathrm{R}\$ 2.50$. What is the lowest cost, in reais, for a person to visit the tops of both viewpoints and return to ground level?
(A) 2.25
(B) 3.90
(C) 4.35
(D) 4.40
(E) 4.45