Question

the area of the base of a cone is 616sq.cm it height is 48 cm then it total surface area is​

Answer 1

Answer:

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=616πr

2

=616

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

7

22

×r

2

=616

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

2

=616×

22

7

r^2=196r

2

=196

Taking square root on both sides, we get

r=14\text{ cm}r=14 cm

Total surface area of a cone is

A=\pi rl+\pi r^2A=πrl+πr

2

A=\pi r\sqrt{r^2+h^2}+\pi r^2A=πr

r

2

+h

2

+πr

2

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

2

=616 .

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

7

22

×14×

14

2

+48

2

+616

A=44\times \sqrt{2500}+616A=44×

2500

+616

A=44\times 50+616A=44×50+616

A=2200+616A=2200+616

A=2816A=2816

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

Answer 2

Given:

• Area of base = 616sq.cm

• Height = 48cm

To Find:  Surface area of the cone.

Solution:

• The formula of the surface area of the cone = $\pi r(r+l)$

• To find that we should first find r and l

• r is the radius of cone which is found by using the formula,

• Area of circle = $\pi r^2$

• 616 = $\pi r^2$

• $r^2$ = 616/$\pi$ = 616/(22/7)  = (616*7)/22 = 196

• r = 14 cm

• l is the slant height which is found by using the formula $l = \sqrt{r^2+h^2}$

• l = $\sqrt{14^2+48^2}$

• l = $\sqrt{196+2304}$

• l = $\sqrt{2500}$

• l = 50 cm

• substituting r and l values in the surface area formula we get,

• surface area = (22/7)*14(14+50) = 2816 $cm^2$

Surface area = 2816$cm^2$