Question

The volume of a solid right circular cone is $4928c{m^3}$ if it’s height is $24cm$ find the radius of the solid cone.

Answer 1

Hint: According to given in the question we have to find the radius of solid cone when the volume of a solid right circular cone is $4928c{m^3}$ if it’s height is $24cm$ so, first of all to find the radius we have to use the formula to find the volume of the given solid cone.
Formula used:
Volume of cone $ = \dfrac{1}{3}\pi {r^2}h$………………..(1)
We can also understand it with the help of the diagram as below:

Where r is the radius of the solid cone which we have to determine and h is the height of the solid cone. So, we will substitute all the values to find the radius of the solid cone in the formula (1)

Complete step-by-step solution:
Given,
Volume of the solid cone = $4928c{m^3}$
Height of the solid cone = $24cm$
Step 1: First of all we have to substitute all the given values in the formula (1) as mentioned in the solution hint.
$ \Rightarrow \dfrac{1}{3} \times \pi \times {r^2} \times 24 = 4928$
Step 2: Now, to solve the expression as obtained in the solution step 1 we have to substitute the value of $\pi $ which is $\dfrac{{22}}{7}$
Hence,
$ \Rightarrow \dfrac{1}{3} \times \dfrac{{22}}{7} \times {r^2} \times 24 = 4928$
Step 3: Now, to solve the obtained expression in step 2 we have to apply the cross-multiplication.
Hence,
$
   \Rightarrow {r^2} = \dfrac{{4928 \times 3 \times 7}}{{22 \times 24}} \\
   \Rightarrow {r^2} = \dfrac{{103488}}{{528}} \\
   \Rightarrow {r^2} = 196 \\
 $
Now, to find the value of r we have to find the square root of 196 hence,
$
   \Rightarrow r = \sqrt {196} \\
   \Rightarrow r = 14cm \\
 $
Hence, with the help of formula (1) as mentioned in the solution hint we have obtained the radius of the solid cone $r = 14cm$

Note: A cone has only one face, which is the circular base but it has no edges and a cone has only one apex or vertex point.
The slant height and total surface area of cone can be obtained by the formulas $l = \sqrt {{r^2} + {h^2}} $ where l is the slant height and $\pi r(l + r)$ is the surface area of the solid cone.