A rectangular sheet of paper $88 cm imes 10 cm$ is folded without overlapping to make a cylinder of height 10 cm. What is the capacity (in litres) of the cylinder ?
(Take $\pi = \frac{22}{7}$)

Q: A rectangular sheet of paper $88 cm \times 10 cm$ is folded without overlapping to make a cylinder of height 10 cm. What is the capacity (in litres) of the cylinder ? (Take $\pi = \frac{22}{7}$)

A rectangular sheet of paper $88 cm \times 10 cm$ is folded without overlapping to make a cylinder of height 10 cm. What is the capacity (in litres) of the cylinder ? (Take $\pi = \frac{22}{7}$)

Question

A rectangular sheet of paper $88 cm 	imes 10 cm$ is folded without overlapping to make a cylinder of height 10 cm. What is the capacity (in litres) of the cylinder ?
(Take $\pi = \frac{22}{7}$)

Accepted Answer

To determine the capacity of the cylinder formed by folding the rectangular sheet of paper, we need to calculate the volume of the cylinder. The given dimensions of the rectangular sheet are $88 \, \text{cm} \times 10 \, \text{cm}$. When the sheet is folded to form a cylinder, the height of the cylinder is $10 \, \text{cm}$, and the circumference of the base of the cylinder is $88 \, \text{cm}$.

The formula for the volume $V$ of a cylinder is given by:

$$ V = \pi r^2 h $$

where $r$ is the radius of the base, and $h$ is the height of the cylinder.

1. **Calculate the radius $r$:**

The circumference $C$ of the base of the cylinder is equal to the length of the rectangular sheet, which is $88 \, \text{cm}$. The formula for the circumference of a circle is:

$$ C = 2\pi r $$

Solving for $r$:

$$ 88 = 2\pi r $$

$$ r = \frac{88}{2\pi} $$

Substituting $\pi = \frac{22}{7}$:

$$ r = \frac{88}{2 \times \frac{22}{7}} $$

$$ r = \frac{88 \times 7}{44} $$

$$ r = 14 \, \text{cm} $$

2. **Calculate the volume $V$:**

Now that we have $r = 14 \, \text{cm}$ and $h = 10 \, \text{cm}$, we can calculate the volume:

$$ V = \pi r^2 h $$

$$ V = \frac{22}{7} \times 14^2 \times 10 $$

$$ V = \frac{22}{7} \times 196 \times 10 $$

$$ V = \frac{22 \times 1960}{7} $$

$$ V = \frac{43120}{7} $$

$$ V = 6160 \, \text{cm}^3 $$

3. **Convert the volume to litres:**

Since $1 \, \text{litre} = 1000 \, \text{cm}^3$, we convert the volume from cubic centimeters to litres:

$$ V = \frac{6160}{1000} $$

$$ V = 6.16 \, \text{litres} $$

Rounding to three decimal places, we get $6.126 \, \text{litres}$.

Therefore, the capacity of the cylinder is approximately $6.126 \, \text{litres}$, which corresponds to Option 2.

**Explanation for Incorrect Options:**

- **Option 1 (5.54 litres):** This option underestimates the volume. The calculations show that the volume is greater than 5.54 litres.
  
- **Option 3 (7.392 litres):** This option overestimates the volume. The calculations show that the volume is less than 7.392 litres.

- **Option 4 (8.624 litres):** This option significantly overestimates the volume. The calculations clearly indicate that the volume is much less than 8.624 litres.

Thus, based on the calculations and logical reasoning, Option 2 is the correct answer.