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

Answer:

3 m

Step-by-step explanation:

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

Given:

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

$\implies \sf 10=\dfrac{1}{3} \cdot 10 \cdot h$

$\implies \sf 10=\dfrac{10}{3}h$

$\implies \sf 30=10h$

$\implies \sf h=\dfrac{30}{10}=3$

Answer 2

Answer:

height: 3 meter

Explanation:

$\sf volume : \frac{1}{3} \ x \ base \ area \ x \ height$

Here given:

• base area: 10 m²

• height: h

• volume: 10 m³

Solve:

$\longrightarrow \sf 10 = \frac{1}{3} \ x \ 10 \ x \ h$

$\longrightarrow \sf 10 = \frac{10}{3} \ x \ h$

$\longrightarrow \sf \frac{10 \ x \ 3}{10} = h$

$\longrightarrow \sf 3 = h$