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** .