Question

Calculate the volume of the composite figure. Round to the nearest tenth.

Answer 1

Volume of the composite figure = 112.6 in³

Explanation:

The composite figure is composed of a cuboid (lower part) and a cylinder( upper part).

The volume of a cuboid is calculated as:

Volume = length × width × height

In this case, the length = 5 in, width = 5 in, and height = 4 in.

Now

Substitute the given value in above formula:

volume of cuboid = 5 × 5 × 4

= 100 in³

Again,

The volume of a cylinder is calculated as:

Volume = πr²h

In this case, the radius (r) = 2 in and the height (h) = 1 in. Therefore, the volume of the cylinder is:

volume of cylinder = π × 2² × 1

= 4π in³

= 12.566370614359 in³

≈ 12.6 in³ in the nearest tenth

To calculate the total volume of the composite figure, we need to add the volumes of the cuboid and the cylinder:

Total volume = volume of cuboid + volume of cylinder

Total volume = 100 in³ + 12.6 in³

Total volume ≈ 112.6 in³

Therefore, the volume of the composite figure is 112.6 cubic inches, rounded to the nearest tenth.

Answer 2

V ≈ 112.6 in³

Explanation:

the figure is composed of a cuboid (lower part ) and a cylinder

the volume of a cuboid is calculated as

volume = length × width × height

here length = 5 in , width = 5 in , height = 4 in , then

volume of cuboid = 5 × 5 × 4 = 100 in³

the volume of a cylinder is calculated as

volume = πr²h ( r is the radius anf h the height )

here r = 2 in and h = 1 in , then

volume of cylinder = π × 2² × 1 = 4π in³

The total volume (V) is the sum of the two solids , that is

V = 100 + 4π ≈ 100 + 12.56 ≈ 112.6 in³ ( to the nearest tenth )