Question

The entire surface of a solid
cone of base radius 3 cm and
height 4 cm is equal to the
entire surface of a solid right
circular cylinder of diameter 4
cm. Find the ratio of their(i)
curved surfaces *​

Answer 1

Question:

The entire surface of a solid cone of base radius 3 cm and height 4 cm is equal to the entire surface of a solid right circular cylinder of diameter 4 cm. Find the ratio of their:

i) Curve surfaces

ii) Volumes

Given:

Measurements of Cone:

Radius = 3cm

Height = 4cm

Measurements of Cylinder:

Radius = 2 cm

To Find:

The ratio of their:

i) Curve surfaces

ii) Volumes

Hint given in question:

Total Surface Area of Cone = Total Surface Area of Cylinder

Solution:

Total Surface Area of Cone:

πr(l+r)

let's find l

√4²+3²

l = 5 cm

πr(l+r)

π3(5+3)

TSA of cone = 24π

Total Surface Area of Cylinder:

24π=2πr(h+r)

24=2×2h+4

12=2h+4

h=4

Now,

i) Ratio of their Curved Surface Area:

Cone : Cylinder

πrl : 2πrh

π×3×5:2π×2×4

15:16

Ratio of their Volumes:

Cone : Cylinder

1/3πr²h:πr²h

1/3π×9×4:π×4×4

12:16

3:4