# VOLUME OF PRISMS AND CYLINDERS WORKSHEET

## About "Volume of Prisms and Cylinders Worksheet"

Volume of Prisms and Cylinders Worksheet :

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

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## Volume of Prisms and Cylinders Worksheet - Problems

Problem 1 :

The box shown below is 5 units long, 3 units wide, and 4 units high. How many unit cubes will fit in the box ? What is the volume of the box ?

Problem 2 :

Find the volume of the right prism shown below.

Problem 3 :

Find the volume of the right cylinder shown below.

Problem 4 :

The volume of the cube shown below is 100 ft3. Find the value of x.

Problem 5 :

The volume of the right cylinder shown below is 4561 m3. Find the value of x.

Problem 6 :

If a concrete weighs 145 pounds per cubic foot, find the weight of the concrete block shown below.

## Volume of Prisms and Cylinders Worksheet - Solutions

Problem 1 :

The box shown below is 5 units long, 3 units wide, and 4 units high. How many unit cubes will fit in the box ? What is the volume of the box ?

Solution :

The base of the box is 5 units by 3 units. This means 5 • 3 or 15 unit cubes, will cover the base.

Solution (a) :

Three more layers of 15 cubes each can be placed on top of the lower layer to fill the box. Because the box contains 4 layers with 15 cubes in each layer, the box contains a total of 4 • 15, or 60 unit cubes.

Solution (b) :

Because the box is completely filled by the 60 cubes and each cube has a volume of 1 cubic unit, it follows that the volume of the box is 60 • 1, or 60 cubic units.

Problem 2 :

Find the volume of the right prism shown below.

Solution :

The area of the base is

B  =  1/2 ⋅ (3)(4)

B  =  6 cm2

The height is

h  =  2 cm

Formula for volume of a right prism is

V  =  Bh

Substitute 6 for B and 2 for h.

V  =  (6)(2)

V  =  12

So, the volume of the right prism is 12 cubic cm.

Problem 3 :

Find the volume of the right cylinder shown below.

Solution :

Formula for volume of a right cylinder is

V  =  πr2h

Substitute 8 for r and 6 for h.

V  =  π(82)(6)

Simplify.

V  =  384π

Use calculator.

V  ≈  1206.37

So, the volume of the right cylinder is about 1206.37 cubic inches.

Problem 4 :

The volume of the cube shown below is 100 ft3. Find the value of x.

Solution :

A side length of the cube is x feet.

Formula for volume of a cube :

V  =  s3

Substitute 100 for V and x for s.

100  =  x3

Take cube root on both sides.

100  =  x

4.64  ≈  x

So, the value of x is about 4.64

Problem 5 :

The volume of the right cylinder shown below is 4561 m3. Find the value of x.

Solution :

Formula for volume of a right cylinder is

V  =  πr2h

Substitute 4561 for V, x for r and 12 for h.

4561  =  πx3(12)

4561  =  12πx3

Divide each side by 12π.

4561/12π  =  x2

Find the positive square root.

11  ≈  x

So, the value of x is about 11.

Problem 6 :

If a concrete weighs 145 pounds per cubic foot, find the weight of the concrete block shown below.

Solution :

To find the weight of the concrete block shown, we need to find its volume.

The area of the base can be found as follows :

B  =  Area larger rectangle - 2 ⋅ Area of small rectangle

B  =  (1.31)(0.66) - 2(0.33)(0.39)

B  ≈  0.61 ft2

Using the formula for the volume of a prism, the volume is

V  =  Bh

V  ≈   0.61(0.66)

V  ≈  0.40 ft3

To find the weight of the block, multiply the pounds per cubic foot, 145 lb/ft3by the number of cubic feet, 0.40 ft3.

Weight  =  [145 lb/ft3⋅ [0.40 ft3]

Simplify.

Weight    58 lb

So, the weight of the concrete block is about 58 pounds.

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