Question

3. Calculate the:RadiusBase Area of the coneVolume of the Cone (solve b only)

Answer 1

• (a)The radius of the cone is 8cm.

,

• (b)The base area of the cone is 200.96 cm².

,

• (c)The volume of the cone is 1004.8 cm³.

Explanation:

(a)Radius

Using the right triangle above, we find the radius of the cone using the Pythagorean theorem.

`\begin{gathered} 17^2=15^2+r^2 \\ r^2=17^2-15^2 \\ r^2=64 \\ r^2=8^2 \\ r=8\text{ cm} \end{gathered}`

The radius of the cone is 8cm.

(b)Base Area of the cone

The base of the cone is a circle.

In part(a), the radius of the circle was found to be 8 cm.

`\begin{gathered} \text{ The area of a circle}=\pi r^2 \\ =3.14*8^2 \\ =200.96\;cm^2 \end{gathered}`

The base area of the cone is 200.96 cm².

(c)Volume of the cone

The volume of a cone is calculated using the formula:

`V=(1)/(3)\pi r^2h`

Substitute the values: π=3.14, h=15cm, r=8cm

`\begin{gathered} V=(1)/(3)*200.96*15 \\ =1004.8\;cm^3 \end{gathered}`

The volume of the cone is 1004.8 cm³.