Question:
If the area of the circular base of a hemisphere is 616 cm², find its volume.
यदि एक अर्धगोले के वृत्ताकार आधार का क्षेत्रफल 616 cm² है, तो इसका आयतन ज्ञात कीजिए।
Options:
- a) 11498.67 cm³
- b) 5749.33 cm³
- c) 22997.33 cm³
- d) 8624.00 cm³
- a) 11498.67 cm³
- b) 5749.33 cm³
- c) 22997.33 cm³
- d) 8624.00 cm³
correct answer : b)
Explanation:
Area of base = pi * r^2 = 616 cm²
=> (22/7) * r^2 = 616 => r^2 = 196 => r = 14 cm.
Volume of a hemisphere = (2/3) * pi * r^3
= (2/3) * (pi * r^2) * r
= (2/3) * 616 * 14 = 17248 / 3 ≈ 5749.33 cm³.
आधार का क्षेत्रफल = pi * r^2 = 616 cm²
=> (22/7) * r^2 = 616 => r^2 = 196 => r = 14 cm.
अर्धगोले का आयतन = (2/3) * pi * r^3
= (2/3) * (pi * r^2) * r
= (2/3) * 616 * 14 = 17248 / 3 ≈ 5749.33 cm³.