4. The South-to-North Water Diversion Project has alleviated water shortages in some northern regions, with part of the water stored in a certain reservoir. When the water level of the reservoir is at an elevation of 148.5 m, the corresponding water surface area is $140.0 \mathrm {~km} ^ { 2 }$; when the water level is at an elevation of 157.5 m, the corresponding water surface area is $180.0 \mathrm {~km} ^ { 2 }$. Treating the shape of the reservoir between these two water levels as a frustum, the volume of water added when the water level rises from an elevation of 148.5 m to 157.5 m is approximately ( $\sqrt { 7 } \approx 2.65$ ) A. $1.0 \times 10 ^ { 9 } \mathrm {~m} ^ { 3 }$ B. $1.2 \times 10 ^ { 9 } \mathrm {~m} ^ { 3 }$ C. $1.4 \times 10 ^ { 9 } \mathrm {~m} ^ { 3 }$ D. $1.6 \times 10 ^ { 9 } \mathrm {~m} ^ { 3 }$
The South-to-North Water Diversion Project has alleviated water shortage problems in some northern regions. Part of the water is stored in a certain reservoir. When the water level is at an elevation of 148.5 m, the corresponding water surface area is $140 \mathrm {~km} ^ { 2 }$ ; when the water level is at an elevation of 157.5 m, the corresponding water surface area is $180 \mathrm {~km} ^ { 2 }$ . Treating the shape of the reservoir between these two water levels as a frustum, the volume of water added when the water level rises from elevation 148.5 m to 157.5 m is approximately ( $\sqrt { 7 } \approx 2.65$ )
4. The South-to-North Water Diversion Project has alleviated water shortages in some northern regions, with part of the water stored in a certain reservoir. When the water level of the reservoir is at an elevation of 148.5 m, the corresponding water surface area is $140.0 \mathrm {~km} ^ { 2 }$; when the water level is at an elevation of 157.5 m, the corresponding water surface area is $180.0 \mathrm {~km} ^ { 2 }$. Treating the shape of the reservoir between these two water levels as a frustum, the volume of water added when the water level rises from an elevation of 148.5 m to 157.5 m is approximately ( $\sqrt { 7 } \approx 2.65$ )\\
A. $1.0 \times 10 ^ { 9 } \mathrm {~m} ^ { 3 }$\\
B. $1.2 \times 10 ^ { 9 } \mathrm {~m} ^ { 3 }$\\
C. $1.4 \times 10 ^ { 9 } \mathrm {~m} ^ { 3 }$\\
D. $1.6 \times 10 ^ { 9 } \mathrm {~m} ^ { 3 }$