Question

The radius and height of cone are in the ratio 4:3. The areas of base 154 find the area the csa

Answer 1

area of base is 154 which is equal to the area of circle ,
area of circle =πr^2=(22(r)^2)/7
154=22(r)^2/7
154*7/22=r^2
1078/22=r^2
49=r^2
r=7
radius is 7 that means height of cone is 21/4
l=√r^2+h^2
l=√49+(441/4)
l=√(49*4+441)/4
l=√(196+441)/4
l=√(637)/4
l=12.61
that means slant height is 12.61.
curved surface area of cone is πrl
=[22(7)(12.61)]/7
=22*12.61
=277.42 unit
I hope it will help you

Answer 2

★ Question ★

$\rule{300}2$

the radius and height of a cone are in ratio 4:3 . the area of the base is 154cm^{2}. find the area of curved surface.

$\rule{300}2$

◇ Answer ◇

radius and height =.4:3

let the unit of ratio be = x

then,

r=4x

h=3x

slant height ( length) =↓

$\implies L^{2}=r^{2}+h^{2} \\ \implies l^{2}=4^{2}+3^{2} \\ \implies l^{2}=16+9 \\ \implies l^{2}=25 \\ \implies l=\sqrt25 \\ \implies = l=5$

★ Area of the base = $πr^{2}$

$\implies 154= \frac{22}{7}×4x^{2}$

$\implies 4x^{2}=\frac{154×7}{22}$

$\implies 4x^{2}=7×7$

$\implies x^{2}=\frac{7×7}{16}$

$\implies x^{2}=\sqrt\frac{7×7}{4×4}$

$\implies x=\frac{7}{4}$

$\implies radius = \frac{7}{4}×4$

$\implies radius = 7cm$

Now,

slant height ↓

$\implies \frac{5×7}{4} \\ \implies \frac{35}{4} cm$

→ C.S.A = πrl

$\implies \frac{22}{7}×7×\frac{35}{4} \\ \implies \frac{776}{4} \\ \implies 192.5cm^{2}$

$\rule{300}2$