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

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Find the volume of the composite space figure to the

mrfluff14

23.01.2022

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,

$V=length \times width \times height$

Substituting the values, we get;

$V=11 \times 9 \times 6$

$V=594 \ mm^3$

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,

$V=\frac{\pi r^2 h}{2}$

Radius of the cylinder = $\frac{9}{2}=4.5$

Height of the cylinder = 11 mm

Substituting the values, we get;

$V=\frac{(3.14)(4.5)^2(11)}{2}$

$V=\frac{699.435}{2}$

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.

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