QUESTION 162
The lateral surface area of a cone with base radius 3 cm and slant height 5 cm is
(A) $10\pi$ cm$^2$
(B) $12\pi$ cm$^2$
(C) $15\pi$ cm$^2$
(D) $18\pi$ cm$^2$
(E) $20\pi$ cm$^2$

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) $\frac{8}{12}$

In building construction, tubes of different sizes are used for water network installation. These measurements are known by their diameter, often measured in inches. Some of these tubes, with measurements in inches, are tubes of $\frac{1}{2}, \frac{3}{8}$ and $\frac{5}{4}$. Placing the values of these measurements in increasing order, we find
(A) $\frac{1}{2}, \frac{3}{8}, \frac{5}{4}$
(B) $\frac{1}{2}, \frac{5}{4}, \frac{3}{8}$
(C) $\frac{3}{8}, \frac{1}{2}, \frac{5}{4}$
(D) $\frac{3}{8}, \frac{5}{4}, \frac{1}{2}$
(E) $\frac{5}{4}, \frac{1}{2}, \frac{3}{8}$

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.

The table presents part of the result of a spermogram (an exam that analyzes the physical conditions and composition of human semen).

\multicolumn{7}{|c|}{Spermogram}
Characteristics	Standard	30/11/2009	23/03/2010	09/08/2011	23/08/2011	06/03/2012
Volume (mL)	2.0 to 5.0	2.5	2.5	2.0	4.0	2.0
Liquefaction time (min)	Up to 60	35	50	60	59	70
pH	7.2 to 7.8	7.5	7.5	8.0	7.6	8.0
Sperm (unit / mL)	$> 20000000$	9400000	27000000	12800000	24200000	10200000
Leukocyte (unit / mL)	Up to 1000	2800	1000	1000	900	1400
Red blood cell (unit / mL)	Up to 1000	800	1200	200	800	800

To analyze the exam, one must compare the results obtained on different dates with the standard value of each evaluated characteristic. The patient obtained a result within the standards in the exam performed on
(A) $30/11/2009$.
(B) $23/03/2010$.
(C) $09/08/2011$.
(D) $23/08/2011$.
(E) $06/03/2012$.

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 water tank in the form of a right rectangular parallelepiped, with 4 m in length, 3 m in width, and 2 m in height, needs to be sanitized. In this operation, the tank will need to be emptied in 20 minutes at most. The water will be removed with the help of a pump with constant flow rate, where flow rate is the volume of liquid that passes through the pump per unit of time.
The minimum flow rate, in liters per second, that this pump should have so that the tank is emptied in the stipulated time is
(A) 2.
(B) 3.
(C) 5.
(D) 12.
(E) 20.

It is intended to build a mosaic with the shape of a right triangle, having three pieces available, two of which are congruent right triangles and the third is an isosceles triangle. The figure presents five mosaics formed by three pieces.
In the figure, the mosaic that has the characteristics of the one intended to be built is
(A) 1.
(B) 2.
(C) 3.
(D) 4.
(E) 5.

For an airplane to be authorized to land at an airport, the aircraft must necessarily satisfy the following safety conditions:
I. the wingspan of the aircraft (greatest distance between the tips of the airplane's wings) must be at most equal to the width of the runway;
II. the length of the aircraft must be less than 60 m;
III. the maximum load (sum of the masses of the aircraft and its cargo) cannot exceed 110 t.
Suppose that the largest runway at this airport is 0.045 km wide, and that the models of airplanes used by airlines that use this airport are given in the table.

Model	Dimensions (length $\times$ wingspan)	Maximum load
A	$44{,}57 \mathrm{~m} \times 34{,}10 \mathrm{~m}$	110000 kg
B	$44{,}00 \mathrm{~m} \times 34{,}00 \mathrm{~m}$	95000 kg
C	$44{,}50 \mathrm{~m} \times 39{,}50 \mathrm{~m}$	121000 kg
D	$61{,}50 \mathrm{~m} \times 34{,}33 \mathrm{~m}$	79010 kg
E	$44{,}00 \mathrm{~m} \times 34{,}00 \mathrm{~m}$	120000 kg

The only aircraft able to land at this airport, according to safety regulations, are those of models
(A) A and C.
(B) A and B.
(C) B and D.
(D) B and E.
(E) C and E.

With the objective of working on concentration and movement synchronization of students in one of his classes, a physical education teacher divided this class into three groups (A, B, and C) and stipulated the following activity: students in group A should clap every 2 s, students in group B should clap every 3 s, and students in group C should clap every 4 s.
The teacher reset the stopwatch and the three groups started clapping when it registered 1 s. The movements continued until the stopwatch registered 60 s.
An intern noted on paper the sequence formed by the instants when the three groups clapped simultaneously.
What is the general term of the sequence noted?
(A) $12n$, with $n$ a natural number, such that $1 \leq n \leq 5$.
(B) $24n$, with $n$ a natural number, such that $1 \leq n \leq 2$.
(C) $12(n-1)$, with $n$ a natural number, such that $1 \leq n \leq 6$.
(D) $12(n-1)+1$, with $n$ a natural number, such that $1 \leq n \leq 5$.
(E) $24(n-1)+1$, with $n$ a natural number, such that $1 \leq n \leq 3$.

On a map with scale 1 : 250 000, the distance between cities A and B is 13 cm. On another map, with scale 1 : 300 000, the distance between cities A and C is 10 cm. On a third map, with scale 1 : 500 000, the distance between cities A and D is 9 cm. The actual distances between city A and cities B, C, and D are, respectively, equal to $X$, $Y$, and $Z$ (in the same unit of length).
The distances $X$, $Y$, and $Z$, in increasing order, are given in
(A) $X, Y, Z$.
(B) $Y, X, Z$.
(C) $Y, Z, X$.
(D) $Z, X, Y$.
(E) $Z, Y, X$.

A blood bank receives 450 mL of blood from each donor. After separating blood plasma from red blood cells, the former is stored in bags with 250 mL capacity. The blood bank rents refrigerators from a company for storage of plasma bags, according to its needs. Each refrigerator has a storage capacity of 50 bags. Over the course of a week, 100 people donated blood to that bank.
Assume that from every 60 mL of blood, 40 mL of plasma is extracted.
The minimum number of freezers that the bank needed to rent to store all the plasma bags from that week was
(A) 2.
(B) 3.
(C) 4.
(D) 6.
(E) 8.

The board of directors of a food company decides to present a proposal for a new product to its shareholders. At this meeting, the average scores given by a group of consumers who tried the new product and two similar competing products (A and B) were presented.
The characteristic that gives the greatest relative advantage to the proposed product and that can be used by the board to encourage its production is
(A) texture.
(B) color.
(C) size.
(D) flavor.
(E) odor.

The package of snacks preferred by a girl is sold in packages with different quantities. Each package is assigned a number of points in the promotion: ``When you total exactly 12 points in packages and add another R\$ 10.00 to the purchase value, you will win a stuffed animal''.
This snack is sold in three packages with the following masses, points, and prices:

\begin{tabular}{ c } Package

mass (g)

&

Package

points

& Price (R\$) \hline 50 & 2 & 2.00 \hline 100 & 4 & 3.60 \hline 200 & 6 & 6.40 \hline \end{tabular}
The smallest amount to be spent by this girl that allows her to take the stuffed animal in this promotion is
(A) R\$ 10.80.
(B) R\$ 12.80.
(C) R\$ 20.80.
(D) R\$ 22.00.
(E) R\$ 22.80.

The owner of a restaurant wants to buy a rectangular glass top for the base of a table, as illustrated in the figure.
It is known that the base of the table, considering the outer edge, has the shape of a rectangle, whose sides measure $AC = 105 \mathrm{~cm}$ and $AB = 120 \mathrm{~cm}$.
At the store where the top will be purchased, there are five types of top options with different dimensions, all with the same thickness, namely:
Type 1: $110 \mathrm{~cm} \times 125 \mathrm{~cm}$
Type 2: $115 \mathrm{~cm} \times 125 \mathrm{~cm}$
Type 3: $115 \mathrm{~cm} \times 130 \mathrm{~cm}$
Type 4: $120 \mathrm{~cm} \times 130 \mathrm{~cm}$
Type 5: $120 \mathrm{~cm} \times 135 \mathrm{~cm}$
The owner evaluates, for user convenience, that one should choose the top with the smallest possible area that satisfies the condition: when placing the top on the base, on each side of the outer edge of the table base, there should be a remaining region, corresponding to a glass frame, limited by a minimum of 4 cm and maximum of 8 cm outside the table base, on each side.
According to the previous conditions, which type of glass top did the owner evaluate should be chosen?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

The venue for Olympic swimming competitions uses the most advanced technology to provide swimmers with ideal conditions. This involves reducing the impact of undulation and currents caused by swimmers in their movement. To achieve this, the competition pool has a uniform depth of 3 m, which helps reduce the ``reflection'' of water (the movement against a surface and the return in the opposite direction, reaching the swimmers), in addition to the already traditional 50 m length and 25 m width. A club wishes to reform its pool of 50 m length, 20 m width and 2 m depth so that it has the same dimensions as Olympic pools.
After the reform, the capacity of this pool will exceed the capacity of the original pool by a value closest to
(A) $20\%$.
(B) $25\%$.
(C) $47\%$.
(D) $50\%$.
(E) $88\%$.

Sodium is present in most industrialized foods and can cause heart problems in people who ingest large quantities of these foods. Doctors recommend that their patients reduce sodium consumption.
Based on nutritional information from five brands of cookies (A, B, C, D and E), a graph was constructed that relates quantities of sodium with portions of different cookies.
Which of the cookie brands presented has the least amount of sodium per gram of product?
(A) A
(B) B
(C) C
(D) D
(E) E