Exercise 5 Page 600

We are given the following solid.

Note that the solid consists of one cone and one cylinder. To find the volume of the solid, we need to find the volumes of the cone and the cylinder. We will start with the cone. Recall that the volume of a cone with the radius r and height h can be calculated by the following formula. V=1/3π r^2 hIn this case, we are given the diameter and the height of the cone. To find the radius, we need to divide the diameter d by 2. Let's do it!

r = d/2

Substitute

d= 10

r = 10/2

CalcQuot

Calculate quotient

r = 5

We got that the radius is equal to 5 centimeters. Therefore, we can substitute the height and the radius into the formula and calculate the volume of the cone.

V=1/3 π r^2 h

SubstituteII

r= 5, h= 4

V=1/3 π ( 5)^2 ( 4)

▼

Simplify right-hand side

CalcPow

Calculate power

V=1/3π(25)(4)

Multiply

Multiply

V= 1/3 * 100 * π

MoveRightFacToNumOne

1/b* a = a/b

V=100π/3

UseCalc

Use a calculator

V=104.719...

RoundDec

Round to 1 decimal place(s)

V≈ 104.7

The volume of the cone is equal to about 104.7 cm^3. Next, we will find the volume of the cylinder. We will 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 The given cylinder has a height of 3 centimeters. Note that the diameter of the cylinder is equal to the diameter of the cone. Therefore, these solids have also the same radius. This means that the radius of the cylinder is 5 centimeters. Let's substitute the height and the radius into the formula and calculate the volume of the cylinder.

V=π r^2 h

SubstituteII

r= 5, h= 3

V=π ( 5)^2 ( 3)

▼

Simplify right-hand side

CalcPow

Calculate power

V=π(25)(3)

Multiply

Multiply

V= π (75)

UseCalc

Use a calculator

V=235.619...

RoundDec

Round to 1 decimal place(s)

V≈ 235.6

The volume of the cylinder is about 235.6 cm^3. Finally, we can calculate the volume of the solid by adding the volumes that we found. 104.7+235.6=340.3 Therefore, the volume of the solid is about 340.3 cm^3.