Courses
Courses for Kids
Free study material
Offline Centres
More
Store

# The CSA of a right circular cylinder of height $14{\text{ cm}}$ is ${\text{88 c}}{{\text{m}}^2}$. Find the radius of the base of the cylinder.

Last updated date: 13th Jun 2024
Total views: 393.3k
Views today: 11.93k
Verified
393.3k+ views
Hint: Here we will use the formula of CSA (Curved surface area) of the cylinder for calculating the radius of the cylinder which equals to as below:
${\text{Curved surface area}} = 2\pi rh$
Where $r$ is known as the radius of the base of the cylinder, $h$ is the height of the cylinder.

Complete step-by-step solution:
Step 1: From the below diagram we can see that the height of the cylinder is given which is $14{\text{ cm}}$ and $r$ is the radius of the base of the cylinder.
${\text{Curved surface area}} = 88{\text{ c}}{{\text{m}}^2}$

Step 2: Now, by using the formula of the curved surface area of the cylinder and by substituting the values of $h = 14{\text{ cm}}$and $\pi = \dfrac{{22}}{7}$ , and ${\text{Curved surface area}} = 88{\text{ c}}{{\text{m}}^2}$, we get:
$88{\text{ c}}{{\text{m}}^2} = 2 \times \dfrac{{22}}{7} \times r \times 14{\text{ cm}}$ ……………. (1)
By dividing $14$ with $7$ into the RHS side of the expression (1), we get:
$\Rightarrow 88{\text{ c}}{{\text{m}}^2} = 2 \times 22 \times r \times 2{\text{ cm}}$
By bringing all the terms of the RHS side into the LHS side in the expression $88 = 2 \times 22 \times r \times 2$ , we get:
$\Rightarrow \dfrac{{88{\text{ c}}{{\text{m}}^2}}}{{2 \times 22 \times 2{\text{ cm}}}} = r$
By dividing into the LHS side we get:
$\Rightarrow 1{\text{ cm}} = r$

$\therefore$ The radius of the base of the cylinder is equal to $1{\text{ cm}}$

Note: Students need to remember some basic formulas for finding surface areas of the cylinder because there are two types of area, one is a Curved surface area and the second is the Total surface area. The formulas for finding both is given below:
${\text{Curved surface area}} = 2\pi rh$
The total surface area of the cylinder$= 2\pi r\left( {r + h} \right)$, where $r$ is known as the radius of the base of the cylinder, $h$ is the height of the cylinder.
Similarly, the formula for finding the volume of the cylinder is as below:
${\text{Volume of the cylinder}} = \pi {r^2}h$