Question

A cylinder has base radius of 7 m and height of 1 m. How much water can it hold? (given: 1000 lt = 1 m\(^3\))

• A. 2,20,000 lt.
• B. 2,15,000 lt.
• C. 1,54,000 lt.
• D. 1,68,000 lt.

Hint:

It's useful to remember common volume conversions: 1 m\(^3\) = 1000 liters and 1 liter = 1000 cm\(^3\). This can save time in mensuration problems involving capacity.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
We need to find the capacity (volume) of a cylinder with a given radius and height, and then convert this volume into liters.
Step 2: Key Formula or Approach:
The formula for the volume (V) of a cylinder is: \[ V = \pi r^2 h \] where 'r' is the radius of the base and 'h' is the height. We will use the approximation \(\pi = \frac{22}{7}\).
Step 3: Detailed Explanation:
Given: - Radius (r) = 7 m - Height (h) = 1 m Calculate the volume in cubic meters (m\(^3\)): \[ V = \frac{22}{7} \times (7)^2 \times 1 \] \[ V = \frac{22}{7} \times 49 \times 1 \] \[ V = 22 \times 7 = 154 \text{ m}^3 \] The capacity of the cylinder is 154 cubic meters.
Now, convert the volume to liters using the given conversion factor (1 m\(^3\) = 1000 lt): \[ \text{Capacity in liters} = 154 \times 1000 = 1,54,000 \text{ lt} \] Step 4: Final Answer:
The cylinder can hold 1,54,000 liters of water.