Find the volume of the composite space figure to the nearest whole number

Question

asked May 6, 2021 163k views

1 Answer

MikeTV · Answer 1 · 2021-05-11T13:53:02+0000

Given:

The composite figure consists of a rectangle and a hemisphere.

The length of the rectangle is 11 mm.

The width of the rectangle is 9 mm.

The height of the rectangle is 6 mm.

We need to determine the volume of the composite figure.

Volume of the rectangle:

The volume of the rectangle can be determined using the formula,

V=length * width * height

Substituting the values, we get;

V=11 * 9 * 6

$V=594 \ mm^3$

Thus, the volume of the rectangle is 594 mm³

Volume of the half of the cylinder:

The volume of the half of the cylinder is given by the formula,

$V=(\pi r^2 h)/(2)$

Radius of the cylinder =
(9)/(2)=4.5

Height of the cylinder = 11 mm

Substituting the values, we get;

V=((3.14)(4.5)^2(11))/(2)

V=(699.435)/(2)

V=349.72

Thus,the volume of the half of the cylinder is 349.72 mm³

Volume of the composite figure:

The volume of the composite figure can be determined by adding the volume of the rectangle and the volume of the half of the cylinder.

Thus, we have;

Volume = Volume of rectangle + Volume of half of the cylinder

Substituting the values, we get;

Volume = 594+349.72

Volume = 943.72

Rounding off to the nearest whole number, we get;

$Volume = 944 \ mm^3$

Thus, the volume of the composite figure is 944 mm³

Hence, Option d is the correct answer.