Question

1. Sum of volume of cylinder (S) and volume of cone (C)
is 2190 t cm² and height of both cylinder and cone is
same i.e, 10 cm. If radius of cone is 15 cm, then find
the ratio of radius of S to radius of C
(a) 1:2 (b) 3:4 (c) 2 : 5 (d) 4:5
(e) 3:5​

Answer 1

Answer:

Let slant height of cone be l

Curved surface area of cylinder=2πrh

Curved surface area of cone=πrl

Ratio=

CSA of cone

CSA of cylinder

=

πrl

2πrh

=

5

8

l

h

=

5

4

Squaring both side

l

2

h

2

=

25

16

l

2

=(

16

25

)h

2

h

2

+r

2

=(

16

25

)h

2

r

2

=(

16

9

)h

2

(

h

r

)

2

=(

4

3

)

2

h

r

=

4

3

Hence ratio of radius to height is 3:4.