The curved surface area of a cylinder is $836 ext{ sq. cm}$, and its height is $19 ext{ cm}$. The radius of the cylinder is $3 ext{ cm}$ less than the side of a square. Find the area of the square in square centimeters.

Question

The curved surface area of a cylinder is $836 	ext{ sq. cm}$, and its height is $19 	ext{ cm}$. The radius of the cylinder is $3 	ext{ cm}$ less than the side of a square. Find the area of the square in square centimeters.

Accepted Answer

**Solution:**

1. Let the side of the square be $x$ cm.

2. The radius of the cylinder is $3$ cm less than the side of the square, so radius $r = x - 3$ cm.

3. The curved surface area (CSA) of a cylinder is given by:
   $$	ext{CSA} = 2 \pi r h$$

4. Substitute the given values:
   $$836 = 2 	imes \frac{22}{7} 	imes (x - 3) 	imes 19$$

5. Simplify the right side:
   $$836 = 2 	imes \frac{22}{7} 	imes 19 	imes (x - 3)$$
   $$836 = \frac{836}{7} 	imes (x - 3)$$

6. Multiply both sides by 7 to clear the denominator:
   $$836 	imes 7 = 836 	imes (x - 3)$$
   $$5852 = 836(x - 3)$$

7. Divide both sides by 836:
   $$x - 3 = \frac{5852}{836} = 7$$

8. Therefore,
   $$x = 7 + 3 = 10 	ext{ cm}$$

9. The area of the square is:
   $$x^2 = 10^2 = 100 	ext{ sq. cm}$$

**Answer:** $100$

Answer

Answer

Answer

Answer