# Volume of cube questions

In this chapter, we will solve questions related to volume of cube.

We know that the formula for volume of cube is given as;

Volume of cube = \mathtt{a^{3}}

Please memorize the formula, as it would help us solve questions.

## Volume of cube solved problems

Question 01
Casey purchased a cubic water tank of size 3 meters. Calculate the amount of water, the tank can hold.

Solution
Volume of tank = \mathtt{3^{3}} = 27 cu. meter.

Hence, the tank can hold 27 cubic meter water.

Question 02
A open cubical box is made of 50 cm thick steel frame. If the external dimension of the cube is 2.5 meter. Find the volume of empty space inside the cube..

Solution
We have to find the dimension of internal box to calculate the volume.

Internal length = 2.5 – 2(0.5) = 1.5 meter

Internal breadth = 2.5 -2(0.5) = 1.5 meter

Internal height = 2.5 – 0.5 = 2 meter
(Since the top is open, we have subtracted by height by 0.5)

Now the internal dimension of the box is 1.5, 1.5 and 2 meter.

Volume of box = 1.5 x 1.5 x 2 = 4.5 cu meter

Hence, the volume of empty space if 4.5 cubic meter.

Question 03
John wants to create a cubical box that can hold 1331 cu. cm of water. What should be the dimension of cube for holding such amount of water.

Solution
Let the size of cube is “a”

Volume of cube = \mathtt{a^{3}}

\mathtt{a^{3} =\ 1331}\\\ \\ \mathtt{a\ =\ 11\ cm\ }

Hence, the size of cube required is 11 cm.

Question 04
Melissa wants to dig a pit in the form of cube of size 6 meters. If the cost of digging is 0.5$per cubic meter. Find the total cost of digging. Solution Volume of pit excavated = 6 x 6 x 6 = 216 cubic meter. Cost of 1 cu meter = 0.5$

Cost of 216 cu meter = 0.5 x 216 = 108 \$

Hence, total cost is 108 dollars.

Question 05
Consider an iron cube of size 50 cm. If a cube of 10 cm is dug out from it, then find the volume of iron left in the main cube.

Solution
Volume of original cube = \mathtt{50^{3} =\ 125000\ cm^{3}}

Volume of dug out cube = \mathtt{10^{3} =\ 1000\ cm^{3}}

Volume left = 125000-1000 = 124000 cu. cm

Question 06
Three iron cubes of 6 cm, 8 cm and 10 cm are melted and then joined to form a bigger cube. Find the dimension of new cube formed.

Solution
First calculate the volume of small cubes.

Volume of 6 cm cube = 6 x 6 x 6 = 216 cu cm

Volume of 8 cm cube = 8 x 8 x 8 = 512 cu cm

Volume of 10 cm cube = 10 x 10 x 10 = 1000 cu cm

All the iron mass are joined together to form single cube.
Total volume = 216 + 512 + 1000 = 1728 cu cm.

Let the side of final cube be ” a “.

Volume of final cube = a x a x a

\mathtt{a^{3} =\ 1728\ cm^{3}}\\\ \\ \mathtt{a\ =\ \sqrt[3]{1728} \ cm\ }\\\ \\ \mathtt{a\ =\ 12\ cm}

Hence, the side of large cube is 12 cm .

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