**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.

Before look at the worksheet, if you would like to learn the stuff about volume of prisms and cylinders,

**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 ft^{3}. Find the value of x.

**Problem 5 : **

The volume of the right cylinder shown below is 4561 m^{3}. 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.

**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 cm^{2}

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 = πr^{2}h

Substitute 8 for r and 6 for h.

V = π(8^{2})(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 ft^{3}. Find the value of x.

**Solution : **

A side length of the cube is x feet.

Formula for volume of a cube :

V = s^{3}

Substitute 100 for V and x for s.

100 = x^{3}

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 m^{3}. Find the value of x.

**Solution : **

Formula for volume of a right cylinder is

V = πr^{2}h

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

4561 = πx^{3}(12)

4561 = 12πx^{3}

Divide each side by 12π.

4561/12π = x^{2}

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 ft^{2}

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

V = Bh

V ≈ 0.61(0.66)

V ≈ 0.40 ft^{3}

To find the weight of the block, multiply the pounds per cubic foot, 145 lb/ft^{3}, by the number of cubic feet, 0.40 ft^{3}.

Weight = [145 lb/ft^{3}] ⋅ [0.40 ft^{3}]

Simplify.

Weight ≈ 58 lb

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

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

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