Question

The slant height of a frustum of a cone is 4cm and the perimeters of its circular ends are 18cm and 16cm then find the curved surface area of the frustum of the cone​

Answer 1

Given:

The slant height of a frustum of a cone is 4cm and the perimeters of its circular ends are 18cm and 16cm.

To find:

Curved surface area of the frustum of cone.

Solution:

As we know,

$\underline{\boxed{CSA_{(frustum)} = π(r_{1} + r_{2}) l}}$

Here, l = 4cm

We have to find $r_{1} \: \& \: r_{2}$

Finding $r_{1}$

Circumference of 1st end = 18cm

$\implies{2πr_{1} = 18}$

$\implies{r_{1} = \frac{18}{2} × \frac{1}{π}}$

$\implies{r_{1} = \frac{9}{2}}$

Finding $r_{2}$

$\implies{2πr_{2} = 6cm}$

$\implies{r_{2} = \frac{6}{2} × \frac{1}{π}}$

$\implies{r_{2} = \frac{3}{π}}$

Now,

$\implies{CSA_{(frustum)} = π(\frac{9+3}{π}) × 4}$

$\implies{CSA_{(frustum)} = π(\frac{12}{π}) × 4}$

$\implies{\red{\mathtt{CSA_{(frustum)} = 48cm³}}}$

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