Question

What is the volume of the composite figure shown? (Use 3.14 for π.)

1,282.17 ft 3
2,000.18 ft 3
1,988.26 ft 3
1,384.74 ft 3

Answer 1

`The\ volume\ of\ the\ cone:V_1=(1)/(3)\pi r^2 H\\(r-a\ radius;\ H-height)\\------------------\\r=7ft;\ H=7ft\\\\V_1=(1)/(3)\pi\cdot7^2\cdot7=(1)/(3)\pi\cdot343=(343)/(3)\pi\ (ft^2)\\-------------------\\The\ volume\ of\ the\ cylinder:V_2=\pi r^2 H\\(r-a\ radius;\ H-height)\\-------------------\\r=7ft;\ H=6ft\\\\V_2=\pi\cdot7^2\cdot6=294\pi\ (ft^3)\\------------------------\\The\ volume\ of\ the\ composite\ figure: V_F=V_1+V_2`


`V_F=(343)/(3)\pi+294\pi=(343)/(3)\pi+(294\cdot3)/(3)\pi=(343)/(3)\pi+(882)/(3)\pi=\boxed{(1225)/(3)\pi\ (ft^3)}\\\\\approx(1225)/(3)\cdot3.14}=(3846.5)/(3)\approx\boxed{1,282.17\ (ft^3)}\leftarrow answer`