The sum of the radius and height of a cylinder is 42 cm. Its total sur

1.	The sum of the radius and height of a cylinder is 42 cm. Its total surface area is 3696 cm 2. What is the volume of cylinder ?1). 17428 cubic cm2). 17248 cubic cm3). 17244 cubic cm4). 17444 cubic cm
Answer» Solution Total surface area of cylinder => $2 \pi r H + 2 \pi r^2 = 3696$ => $2 \pi r (r + h) = 3696$ $\because (r + h) = 42$[Given] => $2 \TIMES \frac{22}{7} \times r \times 42 = 3696$ => $44 \times 6 \times r = 3696$ => $r = \frac{3696}{44 \times 6} = 14$ cm => $h = 42 - 14 = 28$ cm $\THEREFORE$ Volume of cylinder = $\pi r^2 h$ = $\frac{22}{7} \times 14 \times 14 \times 28$ = $17248 cm^3$

The sum of the radius and height of a cylinder is 42 cm. Its total surface area is 3696 cm 2. What is the volume of cylinder ?1). 17428 cubic cm2). 17248 cubic cm3). 17244 cubic cm4). 17444 cubic cm

Answer»

Solution

Total surface area of cylinder

=> $2 \pi r H + 2 \pi r^2 = 3696$

=> $2 \pi r (r + h) = 3696$

$\because (r + h) = 42$[Given]

=> $2 \TIMES \frac{22}{7} \times r \times 42 = 3696$

=> $44 \times 6 \times r = 3696$

=> $r = \frac{3696}{44 \times 6} = 14$ cm

=> $h = 42 - 14 = 28$ cm

$\THEREFORE$ Volume of cylinder = $\pi r^2 h$

= $\frac{22}{7} \times 14 \times 14 \times 28$

= $17248 cm^3$