Question

the radius of two cones are in the ratio of 2:3 and their slant heights are in the ratio of 4:3. Find the ratio of curved surface area
​

Answer 1

✍️Correct Question :

The radius of two cones are in the ratio of 2:3 and their slant heights are in the ratio of 9 : 4 . Find the ratio of curved surface area

✍️AnSwer:

• Ratio of curved surface area is 3 : 2

━━━━━━━━━━━━━━━━━

❇Given:

It is given that radius of the 2 cones are in ratio of 2 : 3 and slant heights are in the ratio of 4 : 3

❇To Find:

• We have to find the ratio of their curved surface area.

❇Solution:

Firstly let us understand the formula to find curved surface area of the cone.

That is,

$\longmapsto { \large{ \boxed{ \bigstar{\sf{ \purple {\: \: CSA = \pi \: rl}}}}}}$

Here, r is base radius of the cone while l is the slant height of the cone.

Now,

★ Ratios are given :

$\longmapsto \sf \: \dfrac{r1}{r2} = \dfrac{2}{3} \\ \\ \longmapsto \sf \: \dfrac{l1}{l2} = \dfrac{9}{4}$

★ Ratio of their CSA:

$\longmapsto \sf \: \: \dfrac{CSA1}{CSA2} = \dfrac{\pi \: r1 \: l1}{\pi \: r2 \: l2} \\ \\ \longmapsto \sf \: \: \dfrac{CSA1}{CSA2} = \dfrac{r1 \: l1}{r2 \: l2} \\ \\ \longmapsto \sf \: \: \dfrac{CSA1}{CSA2} = \dfrac{2}{3} \times \dfrac{9}{4} \\ \\ \longmapsto \sf \: \: \dfrac{CSA1}{CSA2} = \dfrac{3}{2}$

• Hence, ratio of curved surface area of the cone = 3 : 2

━━━━━━━━━━━━━━━━━

✍️Explore more about cones:

• Cone is a three-dimensional structure having a circular base.
• Curved surface area of a cone = πrl
• Total surface area of a cone = πr(l+r)

━━━━━━━━━━━━━━━━━

#TheVenomGirl⚡