A sphere of radius r is cut by a plane at a distance of h from its center,…
20232025
A sphere of radius r is cut by a plane at a distance of h from its center, thereby breaking this sphere into two different pieces. The cumulative surface area of these two pieces is 25% more than that of the sphere. Find h.
- A.
r/√2
- B.
r/√3
- C.
r/√5
- D.
r/√6
Attempted by 1 students.
Show answer & explanation
Correct answer: A
Cumulative area of the two pieces = 25% more than that of sphere.
Area of 2 pieces = 1.25 × 4πr² = 5πr²
Extra area = πr²
Extra area = area of two new circles that are now created circles.
Area each new circle = πr² / 2
Let radius of new circle be r₁.
Now, πr₁² = πr² / 2
r₁ = r / √2
Now, r₁, h and r form a right angled triangle.
h² + r₁² = r²
h² + (r/√2)² = r²
h = r / √2
Choice (A) is therefore, the correct answer.