Question

The radii of the circular ends of a frustum of a cone are 14 cm and 8 cm. If the height of the frustum is 8 cm, find
(1) Slant height of frustum
(2) Total surface area of frustum
(3) Volume of frustum.
(π = 3.14)
​

Answer 1

Question :-

→ Given above ↑

Answer :-

(1) L = 10 cm

(2) TSA = 1507.2 cm²

(3) v = 3117.71 cm³

To Find :-

(1) Slant height

(2) Total surface area (TSA )

(3) Volume (v)

Solution :-

Given that ,

• Height of frustum (h) = 8cm

• r = 14 cm and R = 8 cm

hence ,

(1) Slant height (L)

$\sf \to L = \sqrt{h^{2}+(r - R)^{2}} \\ \\ \to \sf L = \sqrt{ 64 + 36 } \\ \\ </p><p>\to\sf L =\: 10 cm \:$

(2) Total surface area

→ TSA = π(r + R) L + π r² + π R²

→ TSA = 220 π + 196π + 64π

→ TSA = 480 π

→ TSA = 480 × 3.14

→ TSA = 1507.2

(3) Volume

→ v =$\frac{1}{3}\: π (r + R)^{2} \times h$

→ v = $\frac{1}{3} \: π (14 + 8 )^{2} \times 8$

→ v = $\frac{1}{3}\: π \:(22)^{2} \times 8$

→ v = $\frac{1}{3} π \times 3872$

→ v = 3117.71 cm³

Answer 2

${\huge{\underline{\underline{\mathcal {\red{♡Question♡}}}}}}$

The radii of the circular ends of a frustum of a cone are 14 cm and 8 cm. If the height of the frustum is 8 cm, find

(1) Slant height of frustum

(2) Total surface area of frustum

(3) Volume of frustum.

(π = 3.14)

________________________

${\huge{\underline{\underline{\mathcal {\pink{♡Answer♡}}}}}}$

•1.Slant Hieght = 10 cm

•2.TSA = 1507.2 cm²

•3.Volume = 3117.71 cm³

____________________

To Find :-

• Slant height of frustum

• Total surface area of frustum

• Volume of frustum

___________________

${\huge{\underline{\underline{\mathcal {\red{♡Solution♡}}}}}}$

Given,

Height of frustum (h) = 8cm

r = 14 cm and R = 8 cm

hence ,

${\huge{\underline{\underline{\mathcal {\green{♡Height♡}}}}}}$

$\sf \to L = \sqrt{h^{2}+(r - R)^{2}} \\ \\ \to \sf L = \sqrt{ 64 + 36 } \\ \\ </p><p>\to\sf L =\: <strong><em><u>10 cm</u></em></strong> \:$

${\huge{\underline{\underline{\mathcal {\red{♡T.S.A♡}}}}}}$

=> TSA = π(r + R) L + π r² + π R²

=> TSA = 220 π + 196π + 64π

=> TSA = 480 π

=> TSA = 480 × 3.14

=> TSA = 1507.2

${\huge{\underline{\underline{\mathcal {\pink{♡Volume♡}}}}}}$

=> v =$\frac{1}{3}\: π (r + R)^{2} \times h$

=> v = $\frac{1}{3} \: π (14 + 8 )^{2} \times 8$

=> v = $\frac{1}{3}\: π \:(22)^{2} \times 8$

=> v = $\frac{1}{3} π \times 3872$

=> v = 3117.71 cm³

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