Answer:
• (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.
[tex]\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}[/tex]
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.
[tex]\begin{gathered} \text{ The area of a circle}=\pi r^2 \\ =3.14\times8^2 \\ =200.96\;cm^2 \end{gathered}[/tex]
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:
[tex]V=\frac{1}{3}\pi r^2h[/tex]
Substitute the values: π=3.14, h=15cm, r=8cm
[tex]\begin{gathered} V=\frac{1}{3}\times200.96\times15 \\ =1004.8\;cm^3 \end{gathered}[/tex]
The volume of the cone is 1004.8 cm³.
