Question

The solid contains a cone and a hemisphere. Find the volume of the composite solid. (Round your answer to two decimal places.)

____ in3

Answer 1

$volume = \frac{1}{3} \pi {r}^{2} h + \frac{2}{3} \pi {r}^{3} \\ \\ volume = \frac{1}{3} \pi {r}^{2} (h + 2r)$

$volume = \frac{1}{3} \pi \times {7}^{2} \times (10 + 2 \times 7) \\ \\ volume = \boxed{1231.50 \: {in}^{3} }$

Answer 2

The volume of the given solid will be equal to 1231.50 cubic inches.

What is volume?

Volume is defined as the space covered by any solid body in the three-dimensional plane. For semicircle the parameter is radius and for cylinder, the parameters are height and radius.

Given that:-

• The radius of the semicircle is 7 inches.
• The height of the cylinder is 10 inches.

The volume of the solid will be calculated as:-

V   =  Volume of semicircle  +  Volume of cylinder

V   =  $\dfrac{2}{3}\pi r^3+\dfrac{1}{3}\pi r^2h$

V   =  $\dfrac{1}{3}\pi r^2(2r+h)$

V  =  $\dfrac{1}{3}\pi (7)^2\times[ (2\times 7)+10]$

V  =  1231.50 cubic inches

Therefore the volume of the given solid will be equal to 1231.50 cubic inches.

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