# Volume Question

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## Grade 11 Volume CCSS: HSG-MG.A.2

- 170,091 BTU
- 1,471,510 BTU
- 2,041,125 BTU
- 2,387,145 BTU

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Andy has a pool at his house, and he wants to buy a heater for it. Pool heaters are rated by BTU, British Thermal Units. 1 BTU is required to raise the temperature of 1 lb of water by 1°F. Andy's pool is roughly a rectangular prism, with a deeper portion at one end that resembles an inverted truncated square pyramid. The rectangular prism portion of the pool has dimensions of 12 ft by 30 ft, and a depth of 5 ft in the shallow end of the pool. The deeper portion of the pool has a width of 12 ft at its highest point (or 5 ft below the surface of the water) and a width 7 ft at its lowest. The deepest part of the pool, from the surface of the water to the bottom of the pool, is 15 ft. If the density of water is about 8.35 lb/gal, and [math]1 \ "ft"^3 = 7.48 \ "gal"[/math], how much energy, in BTU, would be needed to raise the temperature of the water from 65 °F to 77 °F? Round the answer to the nearest BTU. Hint: the volume of a truncated square pyramid, whose base width is [math]a[/math], whose top width is [math]b[/math], and whose height is [math]h[/math] is given by [math]V = 1/3 (a^2 + ab + b^2)h[/math].

- 170,091 BTU
- 1,471,510 BTU
- 2,041,125 BTU
- 2,387,145 BTU

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