Question

find the height of the cone if its volume is 550cm^3 and its diameter is 10cm​

Answer 1

$\underline{\underline{\textsf{\textbf{ Question\::- }}}}$

Find the height of the cone if its volume is 550 cm^3 and its diameter is 10 cm.

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$\frak{Given}\begin{cases}\sf{\;\;\; diameter\; of \; cone = \bf{10\;cm}}\\\sf{\;\;\;volume\:of\; cone = \bf{500\;cm {3}^{} }}\end{cases}$

$\: \: \:$

$\underline{\underline{\textsf{\textbf{ To Find \::- }}}}$

Height of cone

$\underline{\underline{\textsf{\textbf{ Solution \::- }}}}$

Let , h be the height of cone

$\star\;\boxed{\sf{\red{volume\; of \: _{\;(cone)} \implies \: v = \dfrac{1}{3} \pi r^2h}}}$

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$\implies \: v = \dfrac{1}{3} \times \dfrac{22}{7} \times { 5} \times 5\times h$

$\begin{gathered} \implies \: h = \frac{\cancel5\cancel5\cancel0 \times 3 \times 7}{22 \times \cancel2\cancel5} \\ \implies \: h = \frac{\cancel2\cancel2 \times 3 \times 7}{\cancel2\cancel2} \\ \implies \: h = 21 \: cm\end{gathered}$

${\pink{\bf{height \: of \: the \: cone \: is \: 21 \: cm}}}$

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Answer 2

$\underline\red{\bold{✓EXPLANATION}}$

$\underline\red{\bold{✓GIVEN}}$

• The volume of a cone is 550 cm3 and its diameter is 10 cm

$\underline\red{\bold{✓FORMULA}}$

• The volume of a cone =

$\frac{1}{3} \pi \: {r}^{2} h$

where,

r = radius of cone

h = height of cone

$\underline\red{\bold{✓SOLUTION}}$

• The diameter of cone = 10 cm

so the radius (r) = 10/2 = 5cm

• The volume of cone =

$\begin{gathered} \frac{1}{3} \pi \: {r}^{2}h = 550 \\ \implies \: \frac{1}{3} \times \frac{22}{7} \: {5}^{2} \times h = 550 \\ \implies \: h = \frac{\cancel5\cancel5\cancel0 \times 3 \times 7}{22 \times \cancel2\cancel5} \\ \implies \: h = \frac{\cancel2\cancel2 \times 3 \times 7}{\cancel2\cancel2} \\ \implies \: h = 21 \: cm\end{gathered}$

Hence The height of cone = 21 cm