Question

A cone of height 24cm has a curved surface area 550cm².Find it's volume.

Answer 1

given h=24cm

csa of cone=550cm^2 csa of cone=pi*r*l

pi*R*l=550

r*l=550*7/22

r*l=175

r=175/l

now we know that

l^2=r^2+h^2

l^2=(175/l)^2+24^2

576=l^2–30625/l^2

576=l^4–30625/l^2

l^4–576l^2–30625=0

then suppose x=l^2

then the eq is

x^2–576x-30625=0

x^2–625x+49x-30625=0

x(x-625)+49(x-625)=0

therefore x=625

l=(x)^1/2

l=25cm

r=175/25

r=7cm

volume of cone =1/3 pi*r^2*h

1/3*22/7*49*24

1232cm^3

Answer 2

volume doesn't come in number as they have not given value of slant height or radius