Question

The total surface area of a right circular cylinder is 462 cm².If its curved surface area is on-third of its total surface area, find the valume of the cylinder.

Answer 1

T.S.A of cylinder= 2x pi x r (h +r)=462
                          =r(h+r)=462 x 7/44
                          =r(h+r)= 73.5
                          =rh+r2=73.5........(1)
 C.S.A. of cylinder= 2 x pi x r x h= 154
                            =rh=24.5........(.2)

put value of rh in eq (1)
24.5+r2=73.5
r2=49
r= 7cm
by eq (2) we got h=24.5/7
                           h=3.5cm
so the volume of cylinder is pi x r2 x h
                                          22/7x49x3.5
                                        =3773/7cm3
                                       =3773/7=539 cm3

Answer 2

Let the radius of the base of the cylinder be r
And the height of the cylinder be h

of the cylinder :-
total surface area
= 2x pi x r x h + 2 x pi x r^2

curved surface area= 2 x pi x r x h

ATQ
curved surface area = 1/3 x 462
2 x pi x r x h = 154
2 x 22/7 x r x h = 154
r x h = 154 x 7 / 22 x 2
r x h = 49 / 2---------------(1)
ATQ
total surface area = 2x pi x r x h + 2 x pi x r^2
462 = 2 x 22/7 x r x h + 2 x 22/7 x r^2
44/7 ( rh + r^2) = 462
r x h + r^2 = 147/2
49/2 + r^2 = 147/ 2
r^2 = 147/2 - 49/2
r^2 = 98/2
r^2 = 49
r = 7 [ (-) sign is neglected]

now from (1)
r x h = 49/ 2
7 x h = 49/2
h = 7/2

now volume = pi x r^2 x h
= 22/7 x 49 x 7/2
= 539 cm^3