Question

3. The volume of the cone is 4π dm3 and the diameter of the base is 80 cm. Calculate the cone: the area of the base.

Answer 1

`Area\text{ of the base = 50.24 dm}^2`

Step-by-step explanation:

Given:

Volume of the cone = 4π dm³

diameter of the base = 80cm

To find:

the area of the base

The base of a cone is a circle. Area of the base will be area of the circle

`\begin{gathered} Area\text{ of a circle = \pi r}^2 \\ r\text{ = radius} \end{gathered}`

diameter = 80cm

diameter = 2(radius)

radius = diameter/2

radius = 80/2 = 40 cm

We need to convert from cm to dm to get same units

10cm = 1 dm

40cm = 4 dm

let π = 3.14

substitute the values into the formula:

`\begin{gathered} Area\text{ of the circle = 3.14 }*\text{ 4}^2 \\ Area\text{ of the circle = 50.24} \\ \\ Area\text{ of the base = 50.24 dm}^2 \end{gathered}`