• Question 1
Let's write the formula you will use to find the volume of one cone.
To find the volume of a cone, use the formula below:
[tex]V=\frac{1}{3}\pi r^2\sqrt[]{s^2-r^2}[/tex]Where:
V is the volume
r is the radius of the cone
s is the slant height of the cone
• Question 2:
Let's use the formula above to find the volume of cone B from the given figure.
From cone B, we are given:
Diameter of cone B = 10 cm
Slant height of cone B, s = 10 cm
To find the radius of the cone, divide the diameter by 2:
[tex]\text{Radius, r = }\frac{diameter}{2}=\frac{10}{2}=5\text{ cm}[/tex]Thus, to find the volume, we have:
[tex]V=\frac{1}{3}\pi\ast5^2\sqrt[]{10^2-5^2}[/tex]Solving further, we have:
[tex]\begin{gathered} V=\frac{1}{3}\pi\ast25^{}\sqrt[]{100-25} \\ \\ V=\frac{1}{3}\pi\ast25\sqrt[]{75}^{} \\ \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} V=\frac{1}{3}\pi\ast25\sqrt[]{25\ast3}^{} \\ \\ V=\frac{1}{3}\pi\ast25\sqrt[]{5^2\ast3} \\ \\ V=\frac{1}{3}\pi\ast25\ast5\sqrt[]{3} \\ \\ V=\frac{1}{3}\pi\ast125\sqrt[]{3} \end{gathered}[/tex][tex]\begin{gathered} V=\frac{\pi\ast125\sqrt[]{3}}{3} \\ \\ \text{ V = 226.72 cm}^3 \end{gathered}[/tex]Therefore, the volume of cone B is 226.72 cubic centimeters
