3) Find the height of a cone having the radius of the base as 5 cm and the volume of a cone is \( 44 \mathrm{~cm}^{3} \) ?

To find the height of the cone, we can use the formula for the volume of a cone: \[ V = \frac{1}{3} \pi r^2 h \] Where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height. Plugging in the values we have: \[ 44 = \frac{1}{3} \pi (5^2) h \] \[ 44 = \frac{1}{3} \pi (25) h \] \[ 44 = \frac{25\pi h}{3} \] Now, we can solve for \( h \) by multiplying both sides by 3 and then dividing by \( 25\pi \): \[ h = \frac{44 \times 3}{25\pi} \] \[ h \approx \frac{132}{78.54} \approx 1.68 \text{ cm} \] So, the height of the cone is approximately 1.68 cm. Looking for a little historical flair? Did you know that cones have been used since ancient Egypt for pyramids? They understood the geometric principles behind these shapes long before we did, employing them in architectural marvels that are still studied today! And for a practical tip, when calculating the volume of cones or any 3D shapes, double-check your units. Mixing centimeters, meters, and other measurements can lead to pesky calculation errors. Always be consistent to keep the numbers in check!