The radius of the base and the height of a closed cylinder are in the ratio $ 1 : 3 $. Using $\pi = \frac{22}{

Question

The radius of the base and the height of a closed cylinder are in the ratio $ 1 : 3 $. Using $\pi = \frac{22}{7}$, find its total surface area if its curved surface area is $ 924 	ext{ m}^2 $.

Examoogle · Accepted Answer

The correct answer is Option D: 1232 m^2. Since the radius and height are in the ratio $1:3$, let $r = x$ and $h = 3x$. Substitute directly into the CSA formula to solve for $x$, then calculate the Total Surface Area as $TSA = CSA + 2\pi r^2$.

Step-by-Step Solution & Concepts:
Shortcut Trick: Since the radius and height are in the ratio $1:3$, let $r = x$ and $h = 3x$. Substitute directly into the CSA formula to solve for $x$, then calculate the Total Surface Area as $TSA = CSA + 2\pi r^2$.

Formula Used: $$CSA = 2\pi r h, \quad TSA = 2\pi r(r + h)$$

Given: Ratio of base radius to height of closed cylinder = $1 : 3$, Curved Surface Area ($CSA$) = $924 	ext{ m}^2$, $\pi = \frac{22}{7}$

Steps: Step 1: Assume radius and height from the ratio: Given that the ratio of the radius ($r$) to the height ($h$) is $1 : 3$, we can set $r = x$ and $h = 3x$ for some positive constant $x$.. Step 2: Use the Curved Surface Area (CSA) to find $x$: The formula for the curved surface area of a cylinder is $CSA = 2\pi r h$. Substituting the values, we get $2 	imes \frac{22}{7} 	imes x 	imes 3x = 924$.. Step 3: Solve for $x$ and determine dimensions:

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