Question

1. A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of
radius 6 cm. Find the height of the cylinder.
orm a single​

Answer 1

Solution :-

Let the height of the cylinder be h.

Sphere :-

Radius = 4.2 cm

$\underline{\boxed{\bf Volume \ of \ sphere = \dfrac{4}{3} \pi r^3}}$

$\longrightarrow \sf \dfrac{4}{3} \times \pi \times 4.2 \times 4.2 \times 4.2$

Cylinder :-

Radius = 6 cm

$\underline{\boxed{\bf Volume \ of \ cylinder = \pi r^2h}}$

$\longrightarrow \sf \pi \times 6^2 \times h \\\\\longrightarrow \pi \times 36 \times h$

According to the question :-

Volume of sphere = Volume of cylinder

$\longrightarrow \sf \dfrac{4}{3} \times \pi \times 4.2 \times 4.2 \times 4.2 = \pi \times 36 \times h \\\\\longrightarrow 4 \times \pi \times 4.2 \times 4.2 \times 1.4 = \pi \times 36 \times h \\\\\longrightarrow h = \dfrac{4 \times \pi \times 4.2 \times 4.2 \times 1.4 }{ \pi \times 36 } \\\\\longrightarrow h = \dfrac{4.2 \times 4.2 \times 1.4 }{9} \\\\\longrightarrow h = \dfrac{24.696}{9 } \\\\\longrightarrow \bf h = 2.744$

Height of the cylinder = 2.744 cm