**Q) The slant height of a frustum of a cone is 4 cm and the perimeters of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum.**

**Ans:**

**STEP BY STEP SOLUTION**

Let’s draw a diagram for this question to understand it better:

*[Note: Since a frustum is a combination of 2 cones; hence its curved surface area is difference of curved surface area of 2 cones.]*

**Step 1: **

The Perimeter of a circle, P = 2 π R,

Hence, radius of a circle, R =

Here, we have perimeter of upper circular end, P_{1} = 18 cm

∴ the radius of upper end, R_{1} = =

Similarly, perimeter of lower circular end, P_{2}= 6 cm

∴ the radius of lower end, R_{2} = =

**Step 2:**

Now, the curved surface area of a Frustum is given by: π x L x (R_{1} + R_{2})

Here, we have L = 4 cm, R_{1}= cm, R_{2} = cm,

∴ the curved surface area of given Frustum =

= = 48 cm^{2}

**Therefore, the curved surface area of the frustum is 48 cm ^{2}**

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