Volume of a Prism Worksheet

**Page 1**

1.

A circular hole of diameter $d$ = 3 m is digged on a levelled plot of land shown to a depth of 4 m and the sand so obtained is spread evenly over the rectangular portion of measurement $a$ × $b$ = 7 m × 14 m. What is the increase in the level of the rectangular plot? [Take $\pi $ = 3.]

a. | 36.55 cm | ||

b. | 27.55 cm | ||

c. | 29.55 cm | ||

d. | 33.55 cm |

[Formula.]

Radius =

[Radius =

Height = 4 m = 400 cm.

[Given.]

Volume of the sand = Volume of the hole = 3 × 150

[Volume of cylinder =

Area of the rectangular plot = 700 × 1400 = 980000 cm

[Area =

Increase in the level of the plot =

[Substitute in step 1 and simplify.]

Correct answer : (2)

2.

A circular tank of thickness 30 cm and height 80 cm whose diameter is 4 m is to be constructed in a storage yard. The rate of construction is $10 per m^{3}. Find the cost of construction. [Take $\pi $ = 3.]

a. | $14.94 | ||

b. | $3090 | ||

c. | $284 | ||

d. | $30.90 |

[Radius =

Outer radius of the tank = 200 + 30 = 230 cm

[Radius + thickness of the tank.]

Height of the tank = 80 cm

[Given.]

Volume of the tank = Volume of outer cylinder - Volume of the inner cylinder

[Formula.]

Volume of the outer cylinder = 3 × (230)

[Volume of the cylinder =

Volume of the inner cylinder = 3 × (200)

[Volume of the cylinder =

Volume of the tank = 12696000 - 9600000 = 3096000 cm

[Substitute in step 4.]

Rate of construction = $10 per m

[Given.]

Cost of construction = 3.09 m

[Simplify.]

Correct answer : (4)

3.

A golden bar of length 1.40 m and cross section 18 cm × 18 cm is used to make circular chains of length 64 cm and diameter 6 mm. How many such chains can be made? [Take $\pi $ = 3.]

a. | 2668 | ||

b. | 2625 | ||

c. | 2659 | ||

d. | 2811 |

[Formula.]

Volume of the golden bar = 1.40 × 100 ×18 × 18 = 45360 cm

[Convert meter to centimeter.]

Radius of the chain =

[Radius =

Volume of one chain = 3 × (0.3)

[Volume of a cylinder = π

Number of chains =

[From steps 2 and 4.]

Correct answer : (2)

4.

A medicine is prepared in a tank of side length 1.4 m, width 1 m and depth 3 m. The medicine is filled in cylindrical bottles of diameter 8 cm and height 18 cm. How many bottles can be filled? [Take $\pi $ = 3.]

a. | 10 | ||

b. | 4861 | ||

c. | 49 | ||

d. | 1215 |

[Formula]

Radius of the bottle =

[Radius =

Volume of the bottle = 3 × 4

[Volume of a cylinder =

Volume of the tank = 1.4 × 1 × 3 m³ = 4.2 m³ = 4200000 cm

[Convert meters to centimeters.]

Number bottles =

[From steps 3 and 4.]

Correct answer : (2)

5.

A circular wall of radius 2 m and thickness 30 cm is to be constructed to a total height of 0.8 m. Bricks of measurement 15 cm × 8 cm × 8 cm are to be used. How many bricks would be needed? [Take $\pi $ = 3.]

a. | 3281 | ||

b. | 3312 | ||

c. | 3248 | ||

d. | 3225 |

[Formula.]

Volume of the wall = 3[((2 × 100) + 30)

[Volume of ring =

Volume of the brick = 15 × 8 × 8 = 960 cm

[Volume of the brick =

Number of bricks =

[From steps 2 and 3.]

Correct answer : (4)

6.

A 2 m long cylindrical drum of diameter 1m is lying on its side. A dip-stick is inserted which shows a 30 cm depth of liquid. What volume of liquid is contained in the cylinder?

a. | 0.396 m ^{3} | ||

b. | 0.208 m ^{3} | ||

c. | 0.5652 m ^{3} | ||

d. | 1.317 m ^{3} |

Volume of the liquid = Area of the segment ACB × Length of the drum

[Formula.]

Area of the segment ACB= Area of the sector AOB - Area of the triangle AOB

[From the figure.]

The depth of the water CD is 30 cm

[Given.]

Then OD =

[From the figure.]

cos

[From the figure.]

cos

[Substitute the values.]

Let measure of

Then,

Area of the sector AOB =

[Formula.]

Area of the sector AOB =

[Substitute the values and simplify.]

Area of the triangle AOB = 2 ×

[Since AD = AO sin

Area of the triangle AOB = 2 ×

[Substitute the values: Radius (AO) = 50 cm, OD = 20 cm.]

Area of the segment ACB = 2896.65 - 916.5 = 1980.15 cm

[Substitute in step 2 and simplify.]

Length of the drum = 200 cm

[Given.]

Volume of the liquid = 1980.15 × 200 = 396030 cm

[Substitute in step 1 and simplify.]

Correct answer : (1)

7.

The volume of a rectangular prism is 300 in^{3}. If the width of the prism is 5 in and the height is 6 in, then find the length of the rectangular prism.

a. | 20 in | ||

b. | 27 in | ||

c. | 15 in | ||

d. | 10 in |

[Write an equation.]

=

[Substitute

=

[Multiply 5 and 6.]

= 10 in

[Divide 300 by 30.]

The length of the prism is 10 in.

Correct answer : (4)

8.

The volume of a rectangular prism is 567 cm^{3}. If the width of the prism is 9 cm and the height is 9 cm, what is the length of the rectangular prism?

a. | 9 cm | ||

b. | 8 cm | ||

c. | 10 cm | ||

d. | 7 cm |

=

The length of the prism =

[Substitute the values.]

=

[Multiply 9 by 9.]

= 7 cm

[Divide.]

The length of the prism is 7 cm.

Correct answer : (4)

9.

If the length, width and the height of a rectangular prism are increased 3 times, then the volume of the prism increases _______________.

a. | 28 times | ||

b. | 23 times | ||

c. | 27 times | ||

d. | 18 times |

The volume of the prism =

The new length of the prism = 3

[Since length is increased by 3 times.]

The new width of a prism = 3

[Since width is increased by 3 times.]

The new height of the prism = 3

[Since height is increased by 3 times.]

= 3

The new volume of a prism = length × width × height

[Multiply.]

The volume of the prism increases by 27 times.

Correct answer : (3)

10.

Five copper cubes of sides 8 cm, 5 cm, 4 cm, 4 cm and 1cm are melted to make a single cube. What is the volume of the new cube so formed?

a. | 866 cm ^{3} | ||

b. | 766 cm ^{3} | ||

c. | 22 cm ^{3} | ||

d. | 756 cm ^{3} |

= 8

[Volume of a cube = (side)

= 512 + 125 + 64 + 64 + 1

[Substitute the values and simplify.]

= 766

Volume of the new cube, V = 766 cm

Correct answer : (2)