The diameter of a cone is the diameter of its circular base. It is the distance between any 2 points on the circumference of the base passing through the center. It is denoted by d.
Like radius, it is expressed in mm, cm, m, in, ft, and yd.
Diameter of a Cone
Formula
The formula to calculate the diameter of a cone can be obtained from the formula used to calculate the volume of a cone.
As we know,
Volume ${\left( V\right) =\dfrac{1}{12}\pi d^{2}h}$, here d = diameter, h = height, π = 3.141
Therefore, by rearranging the equation, we can write the formula of diameter as:
${d=2\sqrt{\dfrac{3V}{\pi h}}}$
Solved Examples
Find the diameter of a cone with a volume of 667 cm3 and a height of 13 cm.
Solution:
As we know, ${d=2\sqrt{\dfrac{3V}{\pi h}}}$, here V = 667 cm3, h = 13 cm, π = 3.141 ${\therefore d=2\times \sqrt{\dfrac{3\times 667}{3\cdot 141\times 13}}}$ = 14 cm
Finding the DIAMETER of a cone with SLANT HEIGHT and HEIGHT
Calculate the diameter of a right circular cone with a slant height of 16 mm and a height of 12 mm.
Solution:
Here we will apply the Pythagorean Theorem considering the slant height as hypotenuse and height as the perpendicular leg and find the diameter as the base of a right triangle. ${d=2\sqrt{s^{2}-h^{2}}}$, here s = 16 mm, h = 12 mm, π = 3.141 ${\therefore d=2\sqrt{16^{2}-12^{2}}}$ = 21.16 mm
Finding the DIAMETER of a cone with SLANT HEIGHT and LATERAL SURFACE AREA
Calculate the diameter of a cone with a slant height of 6.5 cm and a lateral surface area of 225 cm2.
Solution:
As we know, r = d/2, we will replace this in the equation of Lateral Surface Area (LSA): ${\because LSA=\pi \dfrac{d}{2}s}$ Rearranging the equation to find d: ${d=2\dfrac{LSA}{\pi s}}$, here LSA = 225cm2, s = 6.5cm, π = 3.141 ${\therefore d=\dfrac{2\times 225}{3.141\times 6\cdot 5}}$ = 22.04 cm
