- The formula for the volume of a cone is:
\[V = \frac { 1} { 3} \pi r^ 2 h\] - Given:
- Diameter = 14 mm, so the radius \(r = \frac { 14} { 2} = 7\) mm.
- Volume \(V = 564.15\) mm\(^ 3\).
- Substitute the known values into the volume formula:
\[564.15 = \frac { 1} { 3} \pi ( 7) ^ 2 h\] - Simplify the equation:
\[564.15 = \frac { 1} { 3} \pi ( 49) h\]
\[564.15 = \frac { 49} { 3} \pi h\]
\[564.15 = 16.3333 \pi h\] - Solve for \(h\):
\[h = \frac { 564.15} { 16.3333 \pi } \]
\[h = \frac { 564.15} { 16.3333 \times 3.14} \]
\[h = \frac { 564.15} { 51.3146} \]
\[h \approx 10.99\] - Round to the nearest whole number:
\[h \approx 11\]
Therefore, the height of the cone is approximately 11 mm.
Supplemental Knowledge
The volume \(V\) of a cone is given by the formula:
\[V = \frac { 1} { 3} \pi r^ 2 h\]
where \(r\) is the radius of the base, \(h\) is the height, and \(\pi \) (pi) is approximately 3.14.
Knowledge in Action
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