Question

3 points
Q.2. The radii of ends of a
frustum are 14 cm and 6 cm
respectively and its height is 6
cm. Find its (i) curved surface
area (ii) total surface area (iii)
volume.
612 cm sq, 1256.12 cm sq, 1843.67 cm
cube
O
628 cm sq, 1356.48 cm sq, 1984.48 cm
cube
513 cm sq, 1278.36 cm sq, 1785.48 cm
cube​

Answer 1

Step-by-step explanation:

$\bf\underline{\underline{\red{Given:-}}}$

• The radii of ends of a frustum are 14cm and 6cm respectively.

• The height of the frustum is 6cm

$\bf\underline{\underline{\blue{To\:Find:-}}}$

• The curved surface area of the frustum

• The total surface area of the frustum

• The volume of the frustum.

$\bf\underline{\underline{\green{Solution:-}}}$

Radii of the frustum are 14cm and 6cm

$\implies \rm r_{1} = 14cm \: \: and \: \: r_{2} = 6cm$

$\rm Height \: (h) = 6cm$

Let the slant height of the frustum be l

$\implies \rm l = \sqrt{ {h}^{2} + {( r_{1} - r_{2}) }^{2} }$

$\implies \rm l = \sqrt{ {6}^{2} + {( 14- 6) }^{2} }$

$\implies \rm l = \sqrt{ {(6)}^{2} + {(8 )}^{2} }$

$\implies \rm l = \sqrt{ 64 + 36 }$

$\implies \rm l = \sqrt{ 100}$

$\implies \underline{ \: \underline{ \rm \: \: \: l = 10cm \: \: \: } \: }$

Now:-

(i) Curved surface Area (CSA) of frustum

$\boxed{ \rm \leadsto CSA\: of \: frustum = \pi l( r_{1} + r_{2}) }$

$\rm = 3.14 \times 10 \times ( 14+ 6)$

$\rm = 3.14 \times 10 \times 20$

$\rm = 628$

$\underline{\boxed{\pink{\rm CSA \: of \: frustum = 628 cm^{2}}}}$

(ii) Total surface area (TSA) of frustum

$\boxed{ \rm \leadsto TSA\: of \: frustum = \pi l( r_{1} + r_{2}) + \pi { r_{1}}^{2} +\pi { r_{2}}^{2} }$

$\rm = 628 + \pi ({ r_{1}}^{2} + { r_{2}}^{2} )$

$\rm = 628 + 3.14 ({ 14}^{2} + { 6}^{2} )$

$\rm = 628 + 3.14 (196 + 36)$

$\rm = 628 + (3.14 \times 232)$

$\rm = 628 + 728.48$

$\rm = 1356.78$

$\underline{\boxed{\orange{\rm TSA \: of \: frustum = 1356.78 cm^{2}}}}$

(iii) Volume of the frustum

$\boxed{ \rm \leadsto Volume\: of \: frustum = \frac{1}{3}\pi h( { r_{1}}^{2} + { r_{2} }^{2} + r_{1} r_{2}) }$

$\rm = \dfrac{1}{3} \times 3.14 \times 6 \times ( {14}^{2} + { 6 }^{2} + 14 \times 6)$

$\rm = \dfrac{1}{3} \times 3.14 \times 6 \times ( 196+ 36 + 84)$

$\rm = \dfrac{1}{3} \times 3.14 \times 6 \times 316$

$\rm = \dfrac{5953.44}{3}$

$\rm = 1984.48$

$\underline{\boxed{\purple{\rm Volume \: of \: frustum = 1984.48 cm^{3}}}}$

We have:-

• CSA of frustum = 628cm²

• TSA of frustum = 1356.48cm²

• Volume of frustum = 1984.48cm³

$\underline{\boxed{\rm Option \: (2) \: is \: correct}}$