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Vera_Pavlovna [14]
3 years ago
5

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

Mathematics
1 answer:
Nimfa-mama [501]3 years ago
7 0
The\ volume\ of\ the\ cone:V_1=\frac{1}{3}\pi r^2 H\\(r-a\ radius;\ H-height)\\------------------\\r=7ft;\ H=7ft\\\\V_1=\frac{1}{3}\pi\cdot7^2\cdot7=\frac{1}{3}\pi\cdot343=\frac{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=\frac{343}{3}\pi+294\pi=\frac{343}{3}\pi+\frac{294\cdot3}{3}\pi=\frac{343}{3}\pi+\frac{882}{3}\pi=\boxed{\frac{1225}{3}\pi\ (ft^3)}\\\\\approx\frac{1225}{3}\cdot3.14}=\frac{3846.5}{3}\approx\boxed{1,282.17\ (ft^3)}\leftarrow answer
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