if the tsa of a solid hemisphere is 462cm2 .find its volume
Answers
Answer:
The volume of hemisphere ≈ 718.67 cm³
Step-by-step explanation:
Given:
- Total surface area of a solid hemisphere = 462 cm²
To find:
- The volume of a solid hemisphere.
Solution:
As we provided with the total surface area of a solid hemisphere, first we will find the radius of a solid hemisphere by using a formula of total surface area of solid hemisphere. After finding the radius, we can simply the formula of volume of hemisphere to find its volume. Putting the values in the formula and then doing the required calculations.
Let's find out...
✰ Total surface area of a solid hemisphere = 3πr²
Where,
Take value of π as 22/7
r is the radius of a solid hemisphere.
Putting the values in the formula, we have:
- 462 = 3 × 22/7 × r²
- 462 = 66/7 × r²
- r² = 462 × 7/66
- r² = 154 × 7/22
- r² = 7 × 7
- r² = 49
- r = √49
- r = 7 cm
∴ The radius of a solid hemisphere = 7 cm
Finally, find out the volume of a solid hemisphere.
✰ Volume of a solid hemisphere = 2/3 πr³
Where,
Take value of π as 22/7
r is the radius of a solid hemisphere which is 7 cm
Putting the values in the formula, we have:
- Volume of a solid hemisphere = 2/3 × 22/7 × 7³
- Volume of a solid hemisphere = 2/3 × 22/7 × 7 × 7 × 7
- Volume of a solid hemisphere = 2/3 × 22/7 × 343
- Volume of a solid hemisphere = 2/3 × 22 × 49
- Volume of a solid hemisphere = 44/3 × 49
- Volume of a solid hemisphere = 2156/3
- Volume of a solid hemisphere ≈ 718.67 cm³
____________________________