Question

The cost of painting the whole surface area of a cube at the rate of 15 paise per square cm is ₹518.40.find the volume of the cube

Answer 1

Let the side of the cube be x
Hence the Total surface area=6a²
=6x²
Cost of painting 1cm²=15paise
Also the cost of painting 6x²×15=518.40
$6 {x}^{2} = \frac{518.40}{100 \times 15} paise$
6x²=3456
x²=3456/6
x=√(576)
x=24cm
Hence the volume of the cube=x³
=24³
=13824cm³

Answer 2

The total cost amount was rs 518.40 or 51840 paisa.

Rate per square cm was 15 paisa.

So the total surface area of the cube be= 51840/15=3456 square cm.

Now if the side of the cube be a, then as per formula total surface area of cube be 6 a^2 which is 3456 square cm.

Now 6a^2 = 3456. a^2 = 3456/6= 576. or a = square root 576 = 24 cm.

Now the volume of cube be side ^3 = a^3 = 24^3 = 13824 cubic centimetres or 13824 cc.