If the total surface area of a hemisphere is \(462\text{cm}^2\) , calculate its radius.
If the total surface area of a hemisphere is \(462\text{cm}^2\) , calculate its radius.
यदि एक अर्धगोले का कुल पृष्ठीय क्षेत्रफल $462 \text{ सेमी}^2$ है, तो उसकी त्रिज्या ज्ञात कीजिए।
Detailed Solution & Logic
Correct Answer:
7 cm
Total surface area of a hemisphere
$= 3\pi r^2$
Given,
$3\pi r^2 = 462$
Using $\pi = \frac{22}{7}$,
$3 \times \frac{22}{7} \times r^2 = 462$
$\frac{66}{7} r^2 = 462$
Multiply both sides by 7:
$66r^2 = 462 \times 7$
$66r^2 = 3234$
$r^2 = 49$
r = 7 cm
Answer: The radius is 7 cm.
Similar Practice Questions
A cubic box with a side length of 30 cm needs to be wrapped with decorative paper made of square pieces, each with a side of 6 cm.
A cubic box with a side length of 30 cm needs to be wrapped with...
In a regular polygon, the number of
In a regular polygon, the number of diagonals is 9. Find the difference between one...
If the surface area of a sphere increases by 21%, by what percentage does its volume increase?
If the surface area of a sphere increases by 21%, by what percentage does its...
A small rectangular container intended for holding liquids has dimensions of 25 cm length, 20 cm width, and 15cm depth.
A small rectangular container intended for holding liquids has dimensions of 25 cm length, 20...
A triangle ABC has a circle inscribed within it with sides a, b, c. The area of the triangle is A. What is the radius of the inscribed circle?
A triangle ABC has a circle inscribed within it with sides a, b, c. The...
If x = $\sqrt{6} + 2 and y =\sqrt{6} – 2$ then what is the value of $(\frac{ x}{y}+\frac{y}{x} )^ 2 – 3 $?
If x = $\sqrt{6} + 2 and y =\sqrt{6} – 2$ then what is the...
A chord of length 24 cm subtends a right angle at the center of the circle. What is the radius of the circle?
A chord of length 24 cm subtends a right angle at the center of the...