Question

A pilgrim is climbing to a temple at top of a conical hill. The hill has equal slope from bottom to top and is 800 meters high from its base. The pilgrim covered the climb at the rate of 2 km/hour in half an hour. What will be the diameter of the base of the hill?

• A. 1800 meters
• B. 1600 meters
• C. 600 meters
• D. 1200 meters

Hint:

For conical hills, the slant height is the actual walking distance. Use Pythagoras with height and slant height to find the radius.

Answer 1

The Correct Option is D

Step 1: Find the slant height climbed.
The pilgrim climbs at 2 km/hr for half an hour: \[ \text{Distance covered} = 2 \times \tfrac{1}{2} = 1 \text{ km} = 1000 \text{ m} \] This 1000 m is the slant height of the conical hill.
Step 2: Use Pythagoras to find the radius.
For a right circular cone: \[ (\text{slant height})^2 = (\text{height})^2 + (\text{radius})^2 \] \[ 1000^2 = 800^2 + r^2 \] \[ 1{,}000{,}000 = 640{,}000 + r^2 \] \[ r^2 = 360{,}000 \] \[ r = 600 \text{ m} \]
Step 3: Calculate the diameter.
\[ \text{Diameter} = 2r = 2 \times 600 = 1200 \text{ m} \]
Step 4: Conclusion.
Thus, the diameter of the base of the hill is 1200 meters, so the correct answer is (D).