Question

3. The volume of the right circular cone is
9856 cu.cm. If the diameter of the base is
28cm. Find the height of the cone?​

Answer 1

To Find :-

The Height of the Cone .

Given :-

• Volume of the Cone = 9856 cm³.

• Diameter of the Cone = 28 cm.

We Know :-

Volume of a Cone :-

$\bf{\underline{V = \dfrac{1}{3}\pi r^{2}h}}$

Where :-

• r = Radius of the cone

• h = Height of the cone

Note :-

The value of π is taken as 22/7.

Concept :-

To find the radius of the base of the cone.

We Know that ,

$\Rightarrow \bf{Radius = \dfrac{Diameter}{2}}$

Given , Diameter = 28 cm.

Putting the value in the diameter , we get :

$\implies \bf{Radius = \dfrac{Diameter}{2}} \\ \\ \implies \bf{Radius = \dfrac{28}{2}} \\ \\ \implies \bf{Radius = 14 cm}$

Hence the Radius of the Cone is 14 cm.

Solution :-

Given :-

• Radius = 14 cm

• π = 22/7

• Volume = 9856 cm³

Taken :-

Let the height be h cm.

Now , using the formula for volume of a Cone and Substituting the values in it ,we get :

$\bf{V = \dfrac{1}{3}\pi r^{2}h} \\ \\ \\ \implies \bf{9856 = \dfrac{1}{3} \times \dfrac{22}{7} \times 14^{2} \times h} \\ \\ \\ \implies \bf{9856 \times 7 = \dfrac{1}{3} \times 22 \times 14^{2} \times h} \\ \\ \\ \implies \bf{9856 \times 7 \times 3 = 22 \times 196 \times h} \\ \\ \\ \implies \bf{\dfrac{9856 \times 7 \times 3}{22} = 196 h} \\ \\ \\ \implies \bf{\dfrac{68992 \times 3}{22} = 196 h} \\ \\ \\ \implies \bf{3136 \times 3 = 196 h} \\ \\ \\ \implies \bf{\dfrac{9408}{196} = h} \\ \\ \\ \implies \bf{48 cm = h} \\ \\ \\ \therefore \purple{\bf{h = 48 cm}}$

Hence, the height of the Cone is 48 cm cm.

Answer 2

$\underline{ \boxed{ \tt cσrrєct \: quєѕtíσn}}$

The volume of the right circular cone is

9856cm³. If the diameter of the base is

28cm.

Find the height of the cone?

$\underline{ \boxed{ \tt αnѕwєr}}$

$\tt✹ \red{GIVEN:-}$

$\tt❂the \: volume \: of \: cone = {9856cm}^{3}$

$\tt❂diameter \: of \: the \: base = 28cm$

$\tt✹ \blue{FIND:-}$

$\tt卐 \: Height \: of \: cone =?$

$\tt✹ \green{SOLUTION:-}$

$\tt⤃Radius = \frac{d}{2} = \frac{ \cancel{24}}{ \cancel2} = 14cm$

$\tt↪we \: know \: volume \: of \: cone = \frac{1}{3} \pi {r}^{2} h$

$\tt now,⇝ \frac{1}{3} \pi {r}^{2} h = 9856 \\ \tt put \: values \: of \: r = 14cm \: and \: \pi = \frac{22}{7} \\ \tt ⇝ \frac{1}{3} \times \frac{22}{7} \times {14}^{2} \times h = 9856 \\ \\ \tt ⇝ \frac{1}{3} \times \frac{22}{ \cancel7} \times \cancel{14} \times 14 \times h = 9856 \\ \tt⇝ \frac{616}{3} h = 9856 \\ \tt ⇝h = \frac{ \cancel{9856} \times 3}{ \cancel{616}} \\ \tt ⇝h = 16 \times 3 = 48cm \\ \tt ⇝h = 48cm$

$\tt Hence, the \: height \: of \: the \: cone \boxed{ \tt ✆ 48cm ✆ }$