Question

The slant height of a frustum of cone is 4 cm and the circumference of its circular ends are 22cm and 10 cm. Find the curved surface area of the frustum .
4 points
64 sq cm
128 sq cm
880 sq cm

Answer 1

Given :

• Slant height of frustum = 4 cm

• Circumference of 1st end = 22 cm

• Circumference of 2nd end = 10 cm

To Find :

• Curved surface area of frustum

Solution :

$\large \implies \boxed{ \sf Circumference = 2\pi r}$

Case 1 :-

$\sf \implies22 = 2 \times \frac{22}{7} \times r_1 \\ \\ \sf \implies22 \times \frac{7}{44} =r_1 \\ \\ \implies \boxed{\sf r_1 = \frac{77}{44} \: cm}$

Case 2 :-

$\sf \implies10 = 2 \times \frac{22}{7} \times r_2 \\ \\ \sf \implies10 \times \frac{7}{44} =r_2 \\ \\ \implies \boxed{\sf r_2 = \frac{70}{44} \: cm}$

Now Curved surface area of frustum is

$\large\implies \boxed{ \boxed{ \sf CSA_{frustum} = \pi(r_1 + r_2)l}} \\\\\sf \implies \frac{22}{7} \times \bigg( \frac{77}{44}+ \frac{70}{44}\bigg) \times 4 \\ \\\sf \implies \frac{22}{7} \times\frac{77 + 70}{44} \times 4\\\\\sf \implies \frac{22}{7} \times\frac{147}{44} \times 4\\\\\sf \implies \frac{1}{7} \times147\times 2 \\ \\ \sf \implies 21 \times 2 \\\\\large\implies \boxed{ \boxed{ \sf CSA_{frustum} = 42 \: {cm}^{2}}}$

Answer 2

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$\Huge{\orange{\underline{\textsf{Answer}}}}$

$\sf\ We \: know \: that$

$\sf\ Circumference \: surface \: area \: of \:frustum = \pi (r_1 + r_2)l$

$\sf\ Here, l = 4 cm$

$\sf\ We \: need \: to \: find \: r_1 \: and \: r_2$

$\rule{200}3$

$\large{\blue{\underline{\tt{For \: r_1}}}}$

$\sf Circumference\:of\:first\:end = 22cm$

$\leadsto$ $\sf\ 2\pi r_1 = 22$

$\leadsto$ $\sf r_1 = \dfrac{22}{2}\times\dfrac{1}{\pi}$

$\leadsto$ $\sf r_1 = \dfrac{11}{\pi}$

$\rule{200}3$

$\large{\red{\underline{\tt{For \: r_2}}}}$

$\sf Circumference\:of\:second\:end = 10cm$

$\leadsto$ $\sf\ 2\pi r_2 = 10$

$\leadsto$ $\sf r_2 = \dfrac{10}{2}\times\dfrac{1}{\pi}$

$\leadsto$ $\sf r_2 = \dfrac{5}{\pi}$

$\rule{200}3$

$\sf\ Now,$

Curved surface area of frustum = $\pi (r_1 + r_2)l$

$\leadsto$$\sf\pi\times\dfrac{11+5}{\pi}\times 4$

$\leadsto$$\sf\pi\times\dfrac{16}{\pi}\times 4$

$\leadsto$$\sf\ 64cm^{2}$

$\rule{200}3$