Question

If the volume of a cone is 10 m^3 what is its height if the area of the base is 10 m^2?

Answer 1

height: 3 meter

Step-by-step explanation:

`\sf volume : (1)/(3) \ x \ base \ area \ x \ height`

Here given:

• base area: 10 m²

• height: h

• volume: 10 m³

Solve:

`\longrightarrow \sf 10 = (1)/(3) \ x \ 10 \ x \ h`

`\longrightarrow \sf 10 = (10)/(3) \ x \ h`

`\longrightarrow \sf (10 \ x \ 3)/(10) = h`

`\longrightarrow \sf 3 = h`

Answer 2

3 m

Step-by-step explanation:

`\textsf{Volume of a cone}=\sf (1)/(3) b h \quad\textsf{(where b is the area of the circular base and h is the height)}`

Given:

• volume = 10 m³
• Area of base = 10 m²

`\implies \sf 10=(1)/(3) \cdot 10 \cdot h`

`\implies \sf 10=(10)/(3)h`

`\implies \sf 30=10h`

`\implies \sf h=(30)/(10)=3`