Question

Find the volume of the entire shape.Round to 2 decimal places.

Answer 1

1488.07 in³

Step-by-step explanation

This shape is formed by two standard shapes: a cone and a half-sphere.

The volume of a cone is,

`V_(cone)=(1)/(3)\pi r^2h`

Where r is the radius of the base and h is the height of the cone.

The volume of a sphere is,

`V_(sphere)=(4)/(3)\pi r^3`

Where r is the radius of the sphere.

In this case, for both the sphere and the cone, the radius is r = 7 inches, and the height of the cone is h = 15 inches. The total volume of the shape is the sum of the volume of the cone and half the volume of the sphere,

`V=V_(cone)+(1)/(2)V_(sphere)`

Let's find the volume of the cone and the sphere,

`\begin{gathered} V_(cone)=(1)/(3)\cdot\pi\cdot7^2in^2\cdot15in\approx769.69in^3 \\ \\ V_(sphere)=(4)/(3)\cdot\pi\cdot7^3in^3\approx\approx1436.76in^3 \end{gathered}`

So the total volume is,

`V=769.69in^3+(1)/(2)\cdot1436.76in^3\approx1488.07in^3`

Hence, the volume of the entire shape is 1488.07 cubic inches.