Question

A solid is in the form of a right circular cylinder with a hemisphere at one end and a cone at the other end. The radius of common base is 3.5 cm and heights of the cylindrical and conical portions are 10 cm and 6 cm respectively. The total surface area of the solid is

• A. $256.72c{m}^2$
• B. $373.45c{m}^2$
• C. $362.76c{m}^2$
• D. $352.65c{m}^2$

Answer 1

The correct option is B $373.45c{m}^2$

Common radius, r = 3.5 cm
Height of conical portion, $h_1=6cm$
Height of cylindrical portion, $h_2=10cm$
Slant height of cone $=l=\sqrt{r^2+h_1^2}$
$=l=\sqrt{{\left(3.5\right)}^2+{\left(6\right)}^2}$
$=\sqrt{12.25+36}$
$=\sqrt{48.25}$
=6.95 cm
Total surface area of given solid = Curved surface area of cone + Curved surface area of cylinder + Curved surface area of hemi-sphere
$\pi rl+2\pi r{h}_2+2\pi r^2$
$=\pi r(l+2h_2+2r)$
$=\frac{22}{7}\times \frac{7}{2}(6.95+2\times 10+2\times \frac{7}{2})$
$=11\times (6.95+20+7)$
$=11\times 33.95$
$=373.45c{m}^2$

So, option b is correct.