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?

  1. A.

    140 cm

  2. B.

    70 cm

  3. C.

    55 cm

  4. 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

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