We are given that a platform is in the shape of the following figure.

A composite solid formed by placing a cylinder between two identical rectangular prisms. The prisms measure 20m x 8m x 5m, while the cylindrical component has a height of 15 m and a base diameter of 8 m.

Note that the figure consists of two rectangular prisms and one cylinder. To find the volume of the figure, we need to find the volumes of the rectangular prisms and the cylinder. We will start with the upper rectangular prism. Recall that the volume of a rectangular prism with length

ℓ,

width

w,

and height

h

can be calculated using the following formula.

V = ℓ w h

We are given that

ℓ = 8,

w = 20,

and

h = 5,

so we have enough information to calculate the volume of the rectangular prism.

V = ℓ w h

SubstituteValues

Substitute values

V = 8 (20) (5)

Multiply

V = 800

The volume of the upper rectangular prism is

800 m^{3} .

Note that the lower rectangular prism has the same measures as the upper prism. Therefore, the volume of the lower rectangular prism is also

800 m^{3} .

Next, we will find the volume of the cylinder. Let's start by recalling that the volume of a cylinder with the radius

r

and height

h

can be calculated by the following formula.

V = π r^{2} h

In this case, we are given the diameter and the height of the cylinder. To find the radius we can divide the diameter

d

by

2 .

r = \frac{d}{2}

Substitute

$d = 8$

r = \frac{8}{2}

CalcQuot

Calculate quotient

r = 4

We got that the radius of the cylinder is

4

meters. Now, we can substitute the height and the radius into the formula and calculate the volume of the cylinder.

V = π r^{2} h

SubstituteII

$r = 4$ , $h = 15$

V = π (4)^{2} (15)

▼

Simplify right-hand side

CalcPow

Calculate power

V = π (16) (15)

Multiply

V = π (240)

UseCalc

Use a calculator

V = 753.982 \dots

RoundInt

Round to nearest integer

V \approx 754

The volume of the cylinder is about

754 m^{3} .

Finally, we can calculate the volume of the platform by adding the volumes that we found.

800 + 800 + 754 = 2354

Therefore, the volume of the platform is about

2354 m^{3} .

Exercise