FIND THE VOLUME AND SURFACE AREA AND LENGTH OF THE CUBE

Problem 1 :

Find the volume of a cube given that the length of its side is :

(a) 4 cm   (b) 6 mm   (c)  2.5 m  (d)  2/3 m

Solution :

(a) Length of the side  a = 4 cm

Volume of a cube = a³

= 4³

= 64 cm³

So, volume of a cube is 64 cm³.

(b) Length of the side a = 6 mm

Volume of a cube = a³

= 6³

= 216 mm³

So, volume of a cube is 216 mm³.

(c) Length of the side a = 2.5 m

Volume of a cube = a³

= (2.5)³

= 15.625 m³

So, volume of a cube is 15.625 m³.

(d) Length of the side a = 2/3 m

2/3 m = (0.67)m

Volume of a cube = a³

= (0.67)³

= 0.300763 m³

So, volume of a cube is 0.300763 m³.

Problem 2 :

A cube has length 10 mm. Find the volume of the cube.

Solution :

Given, cube length a = 10 mm

Volume of a cube = a³

= (10)³

= 1000 mm³

So, volume of a cube is 1000 mm³.

Problem 3 :

The volume of the cube is 729 cm³. Find the length of the cube.

Solution :

Given, volume of the cube = 729 cm³

Volume of a cube = a³

 a³ = 729

a = ∛729

a = 9 cm³

So, length of the cube is 9 cm³.

Problem 4 :

The area of one face of a cube is 36 cm². Find

(a) The length of the cube

(b) The total surface area of the cube

(c) The volume of the cube

Solution :

(a) Area of one face of a cube is 36 cm²

One face of a cube is square.

area = s²

s² = 36

s = 6

(b)

Total surface area = 6a²

36 = 6a²

36/6 = a²

6 = a²

a = √6

a = 2.45 cm

(c) 

Volume of the cube = a³

= (2.45)³

= 14.71 cm³

Problem 5 :

The total surface area of a cube is 294 cm². Find :

(a) The area of one factor of the cube

(b) The length of the cube.

(c) The volume of the cube.

Solution :

Given, the total surface area of a cube =  294 cm²

Surface area of the cube = 6a²

6a² = 294

a² = 294/6

a² = 49

a = 7 cm

(a)  So, the area of one factor of the cube is 7 cm.

(b)

Length of the cube = a³

294 = a³

a = ∛294

a = 6.64

a = 7

So, length of the cube is 7 cm³.

(c)

Volume of the cube = a³

= (7)³

= 343 cm³