Question:
The volume of a solid hemisphere is 486 𝜋 cm³. Find its total surface area.
एक ठोस अर्धगोले का आयतन 486 𝜋 cm³ है। इसका कुल पृष्ठीय क्षेत्रफल ज्ञात कीजिए।
Options:
- a) 243𝜋 cm²
- b) 324𝜋 cm²
- c) 486𝜋 cm²
- d) 162𝜋 cm²
- a) 243𝜋 cm²
- b) 324𝜋 cm²
- c) 486𝜋 cm²
- d) 162𝜋 cm²
correct answer : a)
Explanation:
Volume of a solid hemisphere = (2/3) * pi * r^3
Given: (2/3) * pi * r^3 = 486 * pi
=> r^3 = 486 * 3 / 2 = 729 => r = 9 cm.
Total Surface Area of solid hemisphere = 3 * pi * r^2
= 3 * pi * 9^2 = 3 * pi * 81 = 243pi cm².
ठोस अर्धगोले का आयतन = (2/3) * pi * r^3
दिया गया है: (2/3) * pi * r^3 = 486 * pi
=> r^3 = 486 * 3 / 2 = 729 => r = 9 cm.
ठोस अर्धगोले का कुल पृष्ठीय क्षेत्रफल = 3 * pi * r^2
= 3 * pi * 9^2 = 3 * pi * 81 = 243pi cm².