Question 65

A 36 cm long, 22 cm broad, and 49 cm high cuboid is melted and moulded into a solid sphere. What will be the radius of this sphere? [Use $$\pi = \frac{22}{7}$$]

Solution

Volume of cuboid = Volume of sphere

$$length\times width\times height=\frac{4}{3}\times\pi\times\left(radius\right)^3$$

$$36\times22\times49=\frac{4}{3}\times\frac{22}{7}\times\left(radius\right)^3$$

$$9\times1\times49=\frac{1}{3}\times\frac{1}{7}\times\left(radius\right)^3$$

$$9\times7\times7\times\ 3\times\ 7=\left(radius\right)^3$$

$$3^3\times7^3=\left(radius\right)^3$$
Radius of this sphere = $$7\times3$$ = 21 cm

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