The radius of a cylinder is $ 5 ext{ cm}$ more than its height. If the curved surface area of the cylinder i

Question

The radius of a cylinder is $ 5 	ext{ cm}$ more than its height. If the curved surface area of the cylinder is $ 792 	ext{ cm}^2 $, then the volume of the cylinder (in $	ext{cm}^3 $), is ________. [Use $\pi = \frac{22}{7}$]

Examoogle · Accepted Answer

The correct answer is Option C: 5544. Since the volume formula is $\pi r^2 h$, check which option is divisible by 11 (the factor in $\pi = 22/7$), effectively narrowing down choices quickly.

Step-by-Step Solution & Concepts:
Shortcut Trick: Since the volume formula is $\pi r^2 h$, check which option is divisible by 11 (the factor in $\pi = 22/7$), effectively narrowing down choices quickly.

Formula Used: $$CSA = 2 \pi rh$$, $$V = \pi r^2 h$$

Given: Radius r = h + 5 cm, Curved Surface Area (CSA) = 792 cm^2, Pi = 22/7

Steps: Set up the CSA equation: Given $CSA = 2 \pi rh = 792$ and $r = h + 5$. Substituting these into the CSA formula: $2 	imes \frac{22}{7} 	imes (h + 5) 	imes h = 792$.. Solve for h: Simplify the equation: $(h^2 + 5h) = 792 	imes \frac{7}{44}$. This simplifies to $h^2 + 5h = 126$. Rearranging gives $h^2 + 5h - 126 = 0$.. Factor the quadratic: Factoring $h^2 + 14h - 9h - 126 = 0$ gives $(h + 14)(h - 9) = 0$. Since height cannot be negative, $h = 9$ cm.. Calculate Volume: With $h = 9$, $r = 9 + 5 = 14$ cm. Using the volume formula $V = \pi r^2 h$: $V = \frac{22}{7} 	imes 14^2 	imes 9$.

Answer: Option C is correct because the calculated volume is 5544 cm^3.

Exam Tip: Always ensure the units in mensuration match (cm, cm^2, cm^3) before performing calculations, as this helps prevent scale errors.

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