Question

the radius and height of a cone are in ratio 4 is to 3 the area of its base is 154 cm square find CSA

Answer 1

We have given the ratio of radius and height 4 : 3 Say Radius = 4x Height = 3x Slant Height = root [(4x)2 +(3x)2 ]=5x { as it goes to Pythagorean Theorem}

as we know, Area of Base = pie X radius2 =>154=22/7 X 16x2

so solving the eq we get x=1.75cm

Radius=7 , Height =5.25cm, Slant Height =8.75cm

So csa or Curved Surface Area = pie X radius x slant height = 22/7 X 7 X 8.75 x=192.5cm2 (ans)

Answer 2

★ Question ★

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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.

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◇ 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

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

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