Question

A sphere of 10.5 cm radius is melted and cast into a cuboid of maximum volume. the total surface area of such cuboid is approximately

Answer 1

Since, sphere is melted and casted into a cuboid.

Therefore, the volume of sphere is equal to the volume of cuboid.

Volume of sphere with radius 'r' = $\frac{4}{3} \pi r^3$

It is given radius = 10.5 cm

So, Volume of sphere = $\frac{4}{3} \pi (10.5)^3$

= $\frac{4}{3} \times \frac{22}{7} \times 10.5 \times 10.5 \times 10.5$

= $11 \times 21 \times 21$

As, volume of sphere is equal to volume of cuboid.

$11 \times 21 \times 21$ = $l \times b \times h$

So, l = 11 , b = 21 and h =21

Now, we have to determine the surface area of cuboid

= $2(lb+bh+hl)$

= $2((11 \times 21)+ (21 \times 21)+ (21 \times 11))$

= 1806 square units

So, the total surface area of the cuboid is approximately 1806 square units.