A solid is composed of a cylinder with hemispherical ends.

Question:

A solid is composed of a cylinder with hemispherical ends. If the whole length of the solid is 104 cm and the radius of each hemispherical end is 7 cm, find the surface area of the solid.

Solution:

Radius of the hemispherical end = 7 cm
Height of the hemispherical end = 7 cm

Height of the cylindrical part $=(104-2 \times 7) \mathrm{cm}=90 \mathrm{~cm}$

Surface area of the solid = 2(curved surface area of the hemisphere) + (curved surface area of the cylinder)

$=\left[2\left(2 \pi r^{2}\right)+2 \pi r h\right]$

$=2 \pi r(2 r+h)$

$=2 \times \frac{22}{7} \times 7 \times[(2 \times 7)+90] \mathrm{cm}^{2}$

$=(44 \times 104) \mathrm{cm}^{2}$

$=4576 \mathrm{~cm}^{2}$

 

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