Question 33
Mensuration of SolidsA hollow right prism of equilateral triangular base of side 4cm is filled with water up to a certain height. If a sphere of radius 1/2cm is immersed in the water then the rise of water is
- A.1cm
- B.√3π/24 cm
- C.π/(24√3) cm
- D.24π/√3 cm
- E.24√3 πcm
Show the answer and explanation
Answer: C (π/(24√3) cm)
Explanation
The sphere's volume is (4/3)π(½)³ = π/6. The base area is (√3/4) × 16 = 4√3, so the rise is (π/6) ÷ 4√3 = π/(24√3)cm.