Answer :
Explanation :
the circumference of a circle is given by,
26ft = 2*3.14r
r = 26ft/ 6.28
now, to find the value of the pile ,we first need to determine its volume then multiply it by the value per cubic foot .
volume = 1/3πr^2h
volume = (1/3*3.14*(4.14)^2*10) ft^3
thus, the value of the pile will be equal to
$0.22*179.40
Answer:
$39.47
Step-by-step explanation:
To find the value of the pile of gravel that forms the shape of a cone, multiply the volume of the pile in cubic feet by the value of the gravel per cubic foot.
In this case, we have been given the height and the circumference of the circular base of the cone.
The formula for the circumference of a circle is 2πr, where r is the radius. Given that the circumference is 26 feet, then the radius of the circular base of the cone is:
[tex]2\pi r=26\\\\\\\pi r = 13\\\\\\r=\dfrac{13}{\pi}[/tex]
The formula for the volume of a cone is:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Volume of a Cone}}\\\\V=\dfrac{1}{3}\pi r^2h\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$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:
[tex]r=\dfrac{13}{\pi}[/tex]
[tex]h = 10[/tex]
Substitute the values into the volume formula:
[tex]V=\dfrac{1}{3}\cdot \pi \cdot \left(\dfrac{13}{\pi}\right)^2\cdot 10\\\\\\\\V=\dfrac{\pi}{3}\cdot \dfrac{169}{\pi^2}\cdot 10\\\\\\\\V=\dfrac{10}{3} \cdot \dfrac{169}{\pi}\\\\\\\\V=\dfrac{1690}{3\pi}[/tex]
Substitute 3.14 for π:
[tex]V=\dfrac{1690}{3\cdot 3.14}\\\\\\\\V=\dfrac{1690}{9.42}\\\\\\\\V=\dfrac{169000}{942}[/tex]
To calculate the value of the pile, multiply the volume by the value of $0.22 per cubic foot:
[tex]\textsf{Value}=\dfrac{169000}{942} \times \$0.22\\\\\\\textsf{Value}=\$39.4692144373...\\\\\\\textsf{Value}=\$39.47[/tex]
Therefore, the value of the pile of gravel is:
[tex]\Large\boxed{\boxed{\$39.47}}[/tex]
