Question

ratio of radius and height of cone is 4:3. the area of base is 154 cm² . find bol. of cone

Answer 1

area of base = pi. r^2
154 = 22/7 x r^2
7 x 7 = r^2
r = 7 cm
now ,
given ,
r / h = 4/3
r = (4/3 ) h
h = (3/4) r .

now ,
volume of cone = pi.r^2. h/3
= 22/7 x 7 x 7 x (3/4) x 7 /3
= 22 x 7 x 7 x 1/4
= 77 x 7/2 cm^3
=539/2 = 269.5 cm^3

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

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

$\rule{300}2$