Question

Find the volume of a cone with a diameter of 12 m and a height of 7m.

Answer 1

$\Large \purple \maltese \Huge\: \underline {\rm {{{\color{cyan}{Given...}}}}} \:$

• Diameter = 12
• Radius = 12/2 = 6m
• Height = 7m

$\Large \purple \maltese \Huge\: \underline {\rm {{{\color{cyan}{To \: Find ...}}}}} \:$

• Volume of cone

$\Large \purple \maltese \Huge\: \underline {\rm {{{\color{cyan}{Formula \: Using ...}}}}} \:$

$\Large❏ \: \Large\begin{gathered} {\underline{\boxed{ \sf {{\large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \: \frac{1}{3}\pi {r}^{2} h}}}}}\end{gathered}$

Where,

• r is radius
• h is height

$\Large \purple \maltese \Huge\: \underline {\rm {{{\color{cyan}{Solution ...}}}}} \:$

Substituting the given values in formula.

$\large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \: \frac{1}{3}\pi {r}^{2} h$

$\large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \: \frac{1}{3}\pi {(6)}^{2} \: \times \: 7$

$\large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \: \frac{1}{ \cancel3}\pi \: \times \: \cancel{ 36} \: \: ^{ \pink{12}} \: \times \: 7$

$\large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \:\pi \: \times \: 12 \: \times \: 7$

$\large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \: 84 \pi \: {m}^{3}$

Hence , option b is the correct answer

Answer 2

Answer:

84π m^3

Step-by-step explanation:

1. The formula of a cone is: (1/3) · π · r^2 · h

2. The radius is 6m. (Diameter / 2)

3. (1/3) * π * (6^2) * 7

4. Multiply all numbers besides pi to get the answer in terms of pi

5. (36 / 3 ) = 12 * 7 = 84

6. 84π