Question

How many cylinders of radius 10 cm and height 20 cm can be filled with water from a cylinder of radius 20 cm and height 100 cm full of water?

• A. 30
• B. 60
• C. 20
• D. 40

Answer 1

Answer:

C. 20

20 cylinders of radius 10 cm and height 20 cm can be filled from the larger cylinder.

To find the answer, you divide the volume of the large cylinder by the volume of the small cylinder using the formula for the volume of a cylinder: $V = \pi r^2h$.

1. Volume of Large Cylinder:

   • Radius ($R$) = 20 cm

   • Height ($H$) = 100 cm

   • $\text{Volume}_1 = \pi \times 20^2 \times 100 = \mathbf{40,000\pi\text{ cm}^3}$

2. Volume of Small Cylinder:

   • Radius ($r$) = 10 cm

   • Height ($h$) = 20 cm

   • $\text{Volume}_2 = \pi \times 10^2 \times 20 = \mathbf{2,000\pi\text{ cm}^3}$

3. Number of Cylinders:

   • $\text{Number of cylinders} = \frac{\text{Volume}_1}{\text{Volume}_2}$

   • $\text{Number of cylinders} = \frac{40,000\pi}{2,000\pi} = \mathbf{20}$