Question

plzzz solve it.... ​

Answer 1

$\underline{\sf\ \ \ Given:-\ \ \ }$

Radii of circular ends of frustum of cone is 14cm and 8cm

Height = 8cm

$\underline{\sf\ \ \ To \ Find :-\ \ \ }$

CSA of frustum

TSA of frustum

Volume of frustum

$\underline{\sf\ \ \ SOLUTION :-\ \ \ }$

Curve surface Area of frustum

$\large\underline{\boxed{\sf\ \ CSA\ of \ Frustum= \pi l(R+r)}}$

$\sf{We\ have}\begin{cases}\sf{R=14cm}\\ \sf{r=8cm}\\ \sf{l= \sqrt{h^2+(R-r)^2}}\end{cases}$

$:\implies\sf l= \sqrt{(8)^2+(14-8)^2}\ \ \ \ \big\lgroup h=8cm\big\rgroup\\ \\ \\ :\implies\sf l= \sqrt{64+(6)^2}\\ \\ \\ :\implies\sf l= \sqrt{64+36}\\ \\ \\ :\implies\sf l= \sqrt{100}\\ \\ \\ :\implies\sf Slant \ height (l)= {\boxed{\red{\sf 10cm}}}$

Now CSA of frustum -

$:\implies\sf CSA= \pi l(R+r)\\ \\ \\ :\implies\sf CSA= \dfrac{22}{7}\times 10\times (14+8)\\ \\ \\ :\implies\sf CSA= \dfrac{220\times 22}{7}\\ \\ \\ :\implies\sf CSA= \dfrac{4840}{7}\\ \\ \\ :\implies\sf\ CSA={\underline{\boxed{\purple{\sf 691\dfrac{3}{7}cm^2}}}}$

$\rule{260}{1.2}$

Total Surface Area of frustum -

$\underline{\boxed{\sf\ \ TSA\ of \ Frustum= \pi \Big[ R^2 +r^2+ l(R+r)\Big]}}$

$\sf{We\ have}\begin{cases}\sf{R=14cm}\\ \sf{r=8cm}\\ \sf{l= 10cm}\end{cases}$

$:\implies\sf TSA= \pi\bigg[(14)^2+(8)^2+10(14+8)\bigg]\\ \\ \\ :\implies\sf TSA= \pi \Big[196+64+220\Big]\\ \\ \\ :\implies\sf TSA= \dfrac{22}{7}\times 480\\ \\ \\ :\implies\sf TSA= \dfrac{10560}{7}\\ \\ \\ :\implies\sf TSA={\underline{\boxed{\red{\sf 1508\dfrac{4}{7}cm^2}}}}$

$\rule{260}{1.2}$

Volume of frustum -

$\underline{\boxed{\sf\ \ Volume\ of \ Frustum= \dfrac{\pi h}{3} \Big[ R^2 +r^2+Rr\Big]}}$

$\sf{We\ have}\begin{cases}\sf{R=14cm}\\ \sf{r=8cm}\\ \sf{h= 8cm}\end{cases}$

$:\implies\sf Volume= \dfrac{\pi h}{3}\times \Big[(14)^2+(8)^2+(14\times 8)\Big]\\ \\ \\ :\implies\sf Volume= \dfrac{22\times 8}{7\times 3}\times \Big[196+64+112\Big]\\ \\ \\ :\implies\sf Volume = \dfrac{176}{7\times \cancel{3}}\times \cancel{372}\\ \\ \\ :\implies\sf Volume = \dfrac{176\times 124}{7}\\ \\ \\ :\implies\sf Volume = \dfrac{21824}{7}\\ \\ \\ :\implies\sf Volume= {\underline{\boxed{\pink{\sf 3117\dfrac{5}{7}cm^3}}}}$

Answer 2

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \huge \sf \ \underline{Answer :-}$

(1) L = 10 cm

(2) TSA = 1507.2 cm²

(3) v = 3117.71 cm³

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$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \large \sf \underline \pink{To \: Find :-}$

(1) Slant height

(2) Total surface area (TSA )

(3) Volume (v)

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$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \large\bf \underline \orange{Solution :-}$

Given that ,

• Height of frustum (h) = 8cm

• r = 14 cm and R = 8 cm

hence ,

(1) Slant height (L)

$\begin{gathered}\sf \to L = \sqrt{h^{2}+(r - R)^{2}} \\ \\ \to \sf L = \sqrt{ 64 + 36 } \\ \\ \to\sf L =\: 10 cm \: \end{gathered}$

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(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

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(3) Volume

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

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

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

$→ v = \frac{1}{3} π \times 3872$

$\bf→ v = 3117.71 cm³$

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