Question

If the radius of circular ends of a frustum are 28cm and 7cm and its height is 7cm find the volume of the frustum​

Answer 1

EXPLANATION.

Radius of circular end of frustum are = 28 cm

and 7 cm.

height of frustum = 7 cm

To find the volume of frustum.

$\sf : \implies \: formula \: of \: volume \: of \: frustum \: of \: cone \\ \\ \sf : \implies \: \frac{1}{3}\pi \: h( r_{1} {}^{2} + r_{2} {}^{2} + r_{1} r_{2})$

$\sf : \implies \: \dfrac{1}{3} \times \frac{22}{7} \times 7(28) {}^{2} + (7) {}^{2} + (28 \times 7) \\ \\ \sf : \implies \: \frac{1}{3} \times 22 ( 28 \times 28 + 49 + 196) \\ \\ \sf : \implies \: \frac{1}{3} \times 22(784 + 49 + 196) \\ \\ \sf : \implies \: \frac{1}{3} \times (22 \times 1029) = 7546cm {}^{3}$

$\sf : \implies \: \green{{ \underline{volume \: of \: frustum \: of \: cone \: = 7546 \: cm {}^{3} }}}$

Answer 2

Answer:

EXPLANATION.

Radius of circular end of frustum are = 28 cm

and 7 cm.

height of frustum = 7 cm

To find the volume of frustum.

\begin{gathered}\sf : \implies \: formula \: of \: volume \: of \: frustum \: of \: cone \\ \\ \sf : \implies \: \frac{1}{3}\pi \: h( r_{1} {}^{2} + r_{2} {}^{2} + r_{1} r_{2})\end{gathered}

:⟹formulaofvolumeoffrustumofcone

:⟹

3

1

πh(r

1

2

+r

2

2

+r

1

r

2

)

\begin{gathered}\sf : \implies \: \dfrac{1}{3} \times \frac{22}{7} \times 7(28) {}^{2} + (7) {}^{2} + (28 \times 7) \\ \\ \sf : \implies \: \frac{1}{3} \times 22 ( 28 \times 28 + 49 + 196) \\ \\ \sf : \implies \: \frac{1}{3} \times 22(784 + 49 + 196) \\ \\ \sf : \implies \: \frac{1}{3} \times (22 \times 1029) = 7546cm {}^{3}\end{gathered}

:⟹

3

1

×

7

22

×7(28)

2

+(7)

2

+(28×7)

:⟹

3

1

×22(28×28+49+196)

:⟹

3

1

×22(784+49+196)

:⟹

3

1

×(22×1029)=7546cm

3

\sf : \implies \: \green{{ \underline{volume \: of \: frustum \: of \: cone \: = 7546 \: cm {}^{3} }}}:⟹

volumeoffrustumofcone=7546cm3