Answer :
Answer:
The radius = 2 yards.
Diameter = 4 yards
Step-by-step explanation:
[tex]volume = \frac{1}{3}\pi \: {r}^{2}h[/tex]
where r = radius, h = height and v = volume.
[tex]37.68 = \frac{1}{3} \times 3.14 \times {r}^{2} \times 9[/tex]
[tex]37.68 \times 3 = 3.14 \times {r}^{2} \times 9[/tex]
[tex]113.04 = 28.26 \times {r}^{2} [/tex]
[tex] {r}^{2} = \frac{113.04}{28.26} = 4[/tex]
[tex]r = \sqrt{4} = 2 \: yards[/tex]
The radius = 2 yards.
[tex]diameter = 2 \times radius = 2 \times 2 = 4 \: yards[/tex]
Answer:
Radius = 2 yards
Diameter = 4 yards
Step-by-step explanation:
The formula for the volume of a cone is:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Volume of a Cone}}\\\\V=\dfrac{1}{3}\pi r^2h\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$V$ is the volume.}\\\phantom{ww}\bullet\;\textsf{$r$ is the radius of the circular base.}\\\phantom{ww}\bullet\;\textsf{$h$ is the height.}\end{array}}[/tex]
In this case:
- V = 37.68 yd³
- h = 9 yd
Let's assume that π = 3.14.
To find the radius of the cone, substitute the volume and height into the volume formula and solve for r:
[tex]\dfrac{1}{3}\cdot 3.14\cdot r^2\cdot 9=37.68\\\\\\\dfrac{9}{3}\cdot 3.14 \cdot r^2=37.68\\\\\\3\cdot3.14 \cdot r^2=37.68\\\\\\9.42r^2=37.68\\\\\\r^2=\dfrac{37.68}{9.42}\\\\\\r^2=4\\\\\\r=\sqrt{4}\\\\\\r=2\; \sf yd[/tex]
Therefore, the radius of the circular base of the cone is 2 yards.
As the diameter of a circle is twice its radius, the diameter of the circular base of the cone is 4 yards.
