Question

A wooden cube-shaped box has a total surface area of 486 cm. What is its volume? What will it cost to laminate the outer surface of this box at the rate of Rs 1.50 per sq cm?

Answer 1

Total surface area of the cube-shaped box = 6 × (side)²
or 486 = 6 × (side)²
or $\frac{486}{6}={\left(\mathrm{Side}\right)}^2$ (On dividing both the sides by 6)
or 81 = (side)²
or (9)² = (side)²
or 9 cm = side
∴ Side of the cube-shaped box is 9 cm.
Now, volume of the cube-shaped box = (side)³
= (9)³ cm³
= 729 cm³
Cost of laminating 1 cm² of the outer surface area of the box = Rs 1.50
Cost of laminating 486 cm² of the outer surface area of the box = Rs 1.50 × 486 = Rs 729