# VOLUME OF PRISMS AND CYLINDERS WORKSHEET

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 ? 2. Find the volume of the right prism shown below. 3. Find the volume of the right cylinder shown below. 4. The volume of the cube shown below is 100 ft3. Find the value of x. 5. The volume of the right cylinder shown below is 4561 m3. Find the value of x. 6. If a concrete weighs 145 pounds per cubic foot, find the weight of the concrete block shown below.   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. 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. 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. 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 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. 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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