A steel rod of 4 cm diameter and 14 cm length is used in the making of solid cubical dice. If the length of each side of each dice
is 4 mm, then how many such dice can be made from this rod?
This questions was previously asked in
SSC MTS 7th July 2022 Shift-3
Explanation:
To determine how many dice can be made from the rod:
- Calculate the volume of the rod:
- The rod is cylindrical, with a diameter of 4 cm and length of 14 cm.
- Radius \( r = \frac{4}{2} = 2 \) cm. Convert to millimeters: \( 2 \text{ cm} = 20 \text{ mm} \).
- Length in millimeters: \( 14 \text{ cm} = 140 \text{ mm} \).
- Volume of the cylinder = \(\pi r^2 h = \pi \times 20^2 \times 140\).
- Calculate the volume of one dice:
- Dice side length = 4 mm.
- Volume of one dice = \(4^3 = 64 \) mm³.
- Divide the rod's volume by one dice's volume to find the number of dice:
- Total volume of the rod in mm³ = \(\pi \times 400 \times 140 = 56000\pi\).
- Number of dice = \(\frac{56000\pi}{64}\).
After calculation:
- The number of dice ˜ 2750.
- Option 1: 2750 Correct
- Option 2: 3275
- Option 3: 2250
- Option 4: 2050
.
![]()
By: santosh