**Surface Area of Prisms and Cylinders Worksheet :**

Worksheet given in this section is much useful to the students who would like to practice problems on surface area of prisms and cylinders.

Before look at the worksheet, if you would like to know the basic stuff about surface area of prisms and cylinders,

**Problem 1 : **

Find the surface area of a right rectangular prism with a height of 8 inches, a length of 3 inches, and a width of 5 inches.

**Problem 2 : **

Find the surface area of the right prism shown below.

**Problem 3 : **

Find the surface area of the right prism shown below.

**Problem 4 : **

Find the surface area of the right cylinder shown below.

**Problem 5 : **

Find the height of a cylinder which has a radius of 6.5 centimeters and a surface area of 592.19 square centimeters.

**Problem 1 : **

Find the surface area of a right rectangular prism with a height of 8 inches, a length of 3 inches, and a width of 5 inches.

**Solution : **

Draw a sketch.

The prism has 6 faces, two of each of the following :

The surface area of the prism is

S = 2(40) + 2(24) + 2(15)

S = 80 + 48 + 30

S = 158

So, the surface area of the right rectangular prism is 158 square inches.

**Problem 2 : **

Find the surface area of the right prism shown below.

**Solution : **

Each base measures 5 inches by 10 inches with an area of

B = 5(10)

B = 50 in^{2}

The perimeter of the base is

P = 30 in.

and the height is

h = 6 in.

The surface area is

S = 2B + Ph

S = 2(50) + 30(6)

S = 100 + 180

S = 280

So, the surface area of the right prism is 280 square inches.

**Problem 3 : **

Find the surface area of the right prism shown below.

**Solution : **

In the above prism, each base is an equilateral triangle with a side length s, of 7 meters as shown below.

Using the formula for the area of an equilateral triangle, the area of each base is

B = 1/4 ⋅ √3(s^{2})

B = 1/4 ⋅ √3(7^{2})

B = 1/4 ⋅ 49√3

B = 49√3 / 4 m^{2}

The perimeter of each base is

P = 21 m

and the height is

h = 5 m

The surface area is

S = 2B + Ph

S = 2(49√3/4) + 21(5)

S = 49√3/2 + 105

Use calculator.

S ≈ 147 m^{2}

So, the surface area of the right prism is about 147 square meters.

**Problem 4 : **

Find the surface area of the right cylinder shown below.

**Solution : **

Each base has a radius of 3 feet, and the cylinder has a height of 4 feet.

Formula for surface area of a cylinder :

S = 2πr^{2} + 2πrh

Substitute.

S = 2π(3)^{2} + 2π(3)(4)

S = 18π + 24π

S = 42π

Use calculator.

S ≈ 131.95

So, the surface area of the right cylinder is about 132 square meters.

**Problem 5 : **

Find the height of a cylinder which has a radius of 6.5 centimeters and a surface area of 592.19 square centimeters.

**Solution : **

Draw a sketch.

Formula for surface area of a cylinder :

S = 2πr^{2} + 2πrh

Substitute.

592.19 = 2π(6.5)^{2} + 2π(6.5)(4)

592.19 = 84.5π + 13πh

Subtract 84.5π from each side.

592.19 - 84.5π = 13πh

Simplify.

326.73 ≈ 13πh

Divide each side by 13π.

326.73/13π ≈ h

Use calculator and simplify.

8 ≈ h

So, the height of the cylinder is about 8 cm.

After having gone through the stuff given above, we hope that the students would have understood, "Surface Area of Prisms and Cylinders Worksheet".

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