Question

A tent is of the shape of a right circular cylinder upto a height of $3$ metres and then becomes a right circular cone with maximum height of $13.5$ metres above the ground. If the radius of the base is $14$ metres, the cost of painting the inner side of the tent at the rate of $Rs.2$ per square metre is

• A. $Rs.2050$
• B. $Rs.2060$
• C. $Rs.2068$
• D. $Rs.2080$

Answer 1

The correct option is C $Rs.2068$

Slant height of cone $\left(l\right)$
$=\sqrt{(10.5{)}^2+{14}^2}=\sqrt{110.25+196}$
$=\sqrt{306.25}=17.5metre$
Curved surface area of the cone $=\pi rl$
$=\frac{22}{7}\times 4\times 17.5=770sq.metre$

Curved surface area cylinder $=2\pi rh$
$=2\times \frac{22}{7}\times 14\times 3=264sq.metre$

$\therefore$ Total area $=264+770=1034sq.metre$
$\therefore$ Total cost $=2\times 1034=Rs.2068$.