Word Problems on Volumes of Cubes and Cuboids

Q. A brick has a length of $20$ cm, a width of $10$ cm, and a height of $6$ cm. How many bricks would we need to build a cuboid monument of length $17$ m, width $12$ m, and height $9$ m?

1. $153,000$ cu cm
2. $150,000$ cu cm
3. $1,530,000$ cu cm
4. None of the above

Q.

A stone displaces $10mL$ of water. Its volume is __________.

1. $\frac{1}{100}{m}^3$

2. $\frac{1}{1000}{m}^3$

3. $\frac{1}{10000}{m}^3$

4. $\frac{1}{100000}{m}^3$

Q. If a juice box has a length of $25$ cm, a width of $10$ cm, and a height of $8$ cm, find its volume?

1. 2000

Q. If each small cube in the given figure has a volume of one cubic unit, the volume of the cuboid is cubic units more than that of the cube.

1. $8$
2. $12$
3. $4$

Q. A cubical part of side 10 cm is removed out of a cuboidal solid block with dimensions 11 cm $\times$ 12 cm $\times$ 13 cm. Calculate the volume of the remaining solid.

1. 916 cubic cm
2. 816 cubic cm
3. 1716 cubic cm
4. 716 cubic cm

Q. A wooden block has dimensions $8\text{cm}\times 5\text{cm}\times 5\text{cm}.$ A square hole with dimensions $8\text{cm}\times 2\text{cm}\times 2\text{cm}$ is drilled out of its core.


What is the volume of the remaining wood?

1. $160$ cm${}^3$
2. $164$ cm${}^3$
3. $168$ cm${}^3$
4. $172$ cm${}^3$

Q. Bob has an aquarium that is $80$ cm long, $45$ cm wide, and $40$ cm deep. How much water is needed (in cubic centimeters) to fill it up?

1. $14,000$ cu cm
2. $140,000$ cu cm
3. $144,000$ cu cm

Q. Nancy made a solid shape with cubes and cuboids. Choose the correct option to calculate the volume of the entire solid.

1. Calculate volume of A + B, then B + C + D, then E + D
2. Calculate volume of A, then B + C + D, then E + D
3. Calculate volume of A, then B + C + D, then E
4. Calculate volume of A + B, then B + C + D + A, then E + D

Q. A cubical piece of length 6 cm is cut out of a cubical cake of length 8 cm. Calculate the volume of the remaining cake.

1. 296 cubic cm
2. 396 cubic cm
3. 276 cubic cm
4. 256 cubic cm

Q. Nexus made a cuboidial window with width 2 ft; he made a hole inside it, which has the same width but the other two dimensions are half of the window. Calculate the volume of the remaining window.

1. 73 cubic feet
2. 74 cubic feet
3. 70 cubic feet
4. 72 cubic feet

Q. Luke created a cubical pet house that is 6 inches wide. Calculate the volume of the pet house.

1. 18 cubic inches
2. 36 cubic inches
3. 260 cubic inches
4. 216 cubic inches

Q. Jack made a bird house which has a cuboidial top with dimensions 8 m $\times$ 2 m $\times$ 3 m. In the bottom, he made a entry passage with dimensions 4 m $\times$ 2 m $\times$ 5 m. Calculate the total volume of the bird house.

1. 88 cubic meter
2. 98 cubic meters
3. 78 cubic meters
4. 108 cubic meters

Q. Nexus made a hole of dimensions
2 cm $\times$ 3 cm $\times$ 6 cm through a cube of side 6 cm. Calculate the volume of the remaining cube.

1. 190 cubic cm
2. 170 cubic cm
3. 180 cubic cm
4. 188 cubic cm

Q. A hole of 2 m $\times$ 1 m $\times$ 2m is drilled inside an ice block of 3 m $\times$ 1 m $\times$ 4m to make an ice frame. Calculate the volume of the frame.

1. 7 cubic meters
2. 8 cubic meters
3. 9 cubic meters
4. 10 cubic meters

Q. Out of a cube of length 7 cm, a cubical piece with width 3 cm is removed. Calculate the volume of the remaining solid.

1. 300 cubic cm
2. 316 cubic cm
3. 216 cubic cm
4. 320 cubic cm

Q. A wall of length 9 m is to be built on a ground. The thickness of the wall is 1 m and its height is 12 m. If a brick with dimensions 4m $\times$ 3m $\times$ 1m is removed, calculate the remaining volume of the wall.

1. 108 cubic m
2. 100 cubic m
3. 86 cubic m
4. 96 cubic m

Q.

A stone displaces $10mL$ of water. Its volume is __________.

1. $\frac{1}{100}{m}^3$

2. $\frac{1}{1000}{m}^3$

3. $\frac{1}{10000}{m}^3$

4. $\frac{1}{100000}{m}^3$

Q. For the water passage of of an object,
7 cm $\times$ 6 cm $\times$ 10 cm is drilled out from
4 cm $\times$ 6 cm $\times$ 3 cm.
What is the volume of the remaining solid?

1. 348 cubic cm
2. 290 cubic cm
3. 490 cubic cm
4. 590 cubic cm

Q.

There are guests at Nityas home. They are 8 people in all and Nitya wants to help her mother in the kitchen. She prepares lemonade for the guests.
The recipe for one glass is given:
$○$ $\frac{1}{2}$lemon
$○$ 2 teaspoons of sugar (10 g)
$○$ 1 glass of water (250 ml)
$○$ 4 cubes of ice
How much of each item will be needed to prepare 8 glasses of lemonade (write measures) ?

Q. Sussi made a matchbox which measures 3 cm $\times$ 2 cm $\times$ 5 cm. What will be the volume of a packet containing 10 such boxes?

1. 250 cubic cm
2. 200 cubic cm
3. 300 cubic cm
4. 350 cubic cm

Q. A warehouse measures 18 m × 12 m × 6 m. It is filled with blocks, each measuring 1 m × 2 m × 3 m, completely. If 150 such blocks are removed from the warehouse, find the volume of the remaining blocks.

1. 300 cubic meters
2. 946 cubic meters
3. 390 cubic meters
4. 396 cubic meters