Question

The base area of cone is 616 sq.cm and its height is 48.cm. find its total surface area

Answer 1

base area is =pi r^2 where r=radius of the flat circular base
pir^2=616
or, r=14cm
hence total surface area=616+pi r l=616+ pi*48*14=2727cm^2

Answer 2

Given:

The base area of cone is 616 sq.cm and its height is 48.cm.

To find:

The total surface area of cone.

Solution:

Let r be the radius of cone, h is height and l is slant height of cone.

Height: h=48 cm.

The base area of cone is 616 sq.cm.

$\pi r^2=616$

$\dfrac{22}{7}\times r^2=616$

$r^2=616\times \dfrac{7}{22}$

$r^2=196$

Taking square root on both sides, we get

$r=14\text{ cm}$

Total surface area of a cone is

$A=\pi rl+\pi r^2$

$A=\pi r\sqrt{r^2+h^2}+\pi r^2$

Substitute r=14, h=48 and $\pi r^2=616$.

$A=\dfrac{22}{7}\times14\times \sqrt{14^2+48^2}+616$

$A=44\times \sqrt{2500}+616$

$A=44\times 50+616$

$A=2200+616$

$A=2816$

Therefore, the total surface area of cone is 2816 sq. cm.