Question

the volume of a cone is given as 1/3pir^2h where “r” is the radius of the base’ “h” is the height and “V is the volume. Write an expression for the volume of a cone with a height of 15 units and a radius of 3b units. (leave answer in terms if pi and “b”).

Answer 1

V = 45πb²

Explanation:

The formula for the volume of a cone is given as:

`\large\boxed{V=(1)/(3)\pi r^2 h}`

where:

• V is the volume.
• r is the radius of the circular base.
• h is the height (perpendicular to the base).

To write an expression for the volume of a cone with a height of 15 units and a radius of 3b units, substitute h = 15 and r = 3b into the formula:

`\begin{aligned}V&=(1)/(3)\pi \cdot (3b)^2\cdot 15\\\\V&=(1)/(3)\pi \cdot 3^2b^2\cdot 15\\\\V&=(1)/(3)\pi \cdot 9b^2\cdot 15\\\\V&=(1)/(3)\pi \cdot 135b^2\\\\V&=(135)/(3)\pi\cdot b^2 \\\\V&=45\pi b^2 \end{aligned}`

Therefore, the expression for the volume of a cone with a height of 15 units and a radius of 3b units is:

`\Large\boxed{V=45 \pi b^2}`