Question

csa of a cone is 308cm² and its base radius is 7cm .Find=volume or total surface area​

Answer 1

Curved surface area of a cone. is 308 cm2 its slant height is 14 cm. Find

(i) radius of the base and

(ii) total surface area of the cone.

Curved surface area of the cone =308cm2 and Slant height or l=14 cm.

Curved surface area of the cone =πrl

308=722×r×14

r=(22×14)(308×7)

r=7cm

Total surface area of the cone =πr(r+l)

=(722×7)(7+14)

=22×21

Total surface area of the cone =462cm2

So, the radius of the base of the cone is 7 cm and the total surface area of the cone is 462cm2.

Answer 2

CSA of cone = 308 $cm^{2}$, radius,r = 7cm

πrl = 308

$\frac{22}{7} * 7 * l= 308$

$l = \frac{308}{22}$

$l = 14$

$l = 14$, slant height, l = 14 cm.

radius = 7cm, slant height = 14cm

total surface area = πr ( l + r )

= $\frac{22}{7} * 7 ( 7 + 14)$

$= 22(21)$ = 462$cm^2$

height = $\sqrt{ l^{2} - r^2}$

= $\sqrt{14^2 - 7^2} = \sqrt{196 - 49} = \sqrt{147} = 7\sqrt{3}cm$

volume of cone = $\frac{1}{3}$ * π$r^{2} h$

= $\frac{1}{3} * \frac{22}{7} * 7^{2} * 7\sqrt{3}$  = $\frac{22 * 7 * 7 }{\sqrt{3} }$  = $\frac{1078}{\sqrt{3} }$ = $\frac{1078}{1.732}$ = 622.4$cm^{3}$

volume = 622.4$cm^{3}$

total surface area = 462 $cm^2$

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