Question

What is the volume of the composite figure? (Round to the nearest hundredth. Use 3.14 for x.)

Answer 1

The volume of the composite figure is the third option 385.17 cubic centimeters.

Step-by-step explanation:

Step 1:

The composite figure consists of a cone and a half-sphere on top.

We will have to calculate the volumes of the cone and the half-sphere separately and then add them to obtain the total volume.

Step 2:

The volume of a cone is determined by multiplying $\frac{1}{3}$ with π, the square of the radius (r²) and height (h). Here we substitute π as 3.1415.

The radius is 4 cm and the height is 15 cm.

The volume of the cone :

$V = \frac{1}{3} \pi r^{2} h = \frac{1}{3} (3.1415)(4^{2} )(15) = 251.32$ cubic cm.

Step 3:

The area of a half-sphere is half of a full sphere.

The volume of a sphere is given by multiplying $\frac{4}{3}$ with π and the cube of the radius (r³).

Here the radius is 4 cm. We take π as 3.1415.

The volume of a full sphere $\frac{4}{3} \pi r^{3} = \frac{4}{3} (3.1415) (4^{3}) = 268.07$ cubic cm.

The volume of the half-sphere $=\frac{1}{2} (268.07) = 134.037$ cubic cm.

Step 4:

The total volume = The volume of the cone + The volume of the half sphere,

The total volume $251.32+134.037 = 385.357$ cub cm. This is closest to the third option 385.17 cubic centimeters.