Question

the curved surface area of cylinder is 2640 square and its volume is 26400 cm find the curved surface area of a right circular cone which has the same base and height of the cylinder​

Answer 1

Therefore the surface area of a right circular cone is = 4179.5$cm^2$

Step-by-step explanation:

Given

The curved surface area of cylinder is 2640 $cm^2$ and its volume is 26400 $cm^3$

According to problem

$2\pi r h= 2640$ .......(1)            and        $\pi r^2 h = 26400$.........(2)

Dividing equation (2) by equation (1)

$\frac{\pi r^2h }{2\pi rh} =\frac{26400}{2640}$

⇔r=20 cm

Putting the value of r in equation (1)

$2 \pi \times20 \times h= 2640$

⇔h =$\frac{2640}{\pi 20 }$

⇔h = 42 cm

Therefore the surface area of a right circular cone is = $\pi r [{r + \sqrt{h^{2}+ r^{2} } } ]$

= 4179.5$cm^2$ (approx) [ here r=20 cm and h = 42 cm]