Six times of the volume of a sphere is 29106 cm3. What will be the ten times…
2021
Six times of the volume of a sphere is 29106 cm3. What will be the ten times of the radius of the sphere?
- A.
140 cm
- B.
70 cm
- C.
55 cm
- D.
105 cm
Attempted by 2 students.
Show answer & explanation
Correct answer: D
To find the ten times of the radius of the sphere, we first need to determine the radius itself using the given information.
Step-by-Step Calculation
Use the given volume information:
We are told that six times the volume of a sphere is 29,106 cubic centimetres.
6 * V = 29,106
V = 29,106 / 6
V = 4,851 cubic centimetres
Calculate the radius (r):
The formula for the volume of a sphere is V = (4/3) * π * r³.
Using π = 22/7:
4,851 = (4/3) * (22/7) * r³
4,851 = (88 / 21) * r³
r³ = (4,851 * 21) / 88
r³ = 101,871 / 88
r³ ≈ 1,157.6
(Note: Based on standard sphere volume problems of this type, if V = 4851, r is typically 10.5 cm. Let's verify: 4/3 * 22/7 * 10.5³ = 4851. Yes, that is correct.)
r = 10.5 cm
Find ten times the radius:
10 * r = 10 * 10.5
10 * r = 105 cm