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A sphere and a right circular cylinder of the same radius have equal volumes. By what percentage does the diameter of the cylinder exceed its height?

Solution:

Given, a sphere and a right circular cylinder have same radius and equal volumes

We have to find by what percentage does the diameter of the cylinder exceed its height.

Let, radius of sphere = radius of right circular cylinder = r

Given, volume of sphere = volume of right circular cylinder

Volume of sphere = 4/3 πr³

Where, r is the radius of the sphere

Volume of cylinder = πr²h

Where, r is the radius of the cylinder

h is the height of the cylinder

So, 4/3 πr³ = πr²h

4/3 r = h

Now, h = 4/3 r

Diameter of the cylinder = 2r

Increased diameter = 2r - 4/3 r

= (6r - 4r)/3

= 2r/3

Percentage increase in diameter of the cylinder = (increased diameter / height of the cylinder) × 100

= [(2r/3)/(4r/3)] × 100

= 100/2

= 50%

Therefore, the percentage increase is 50%

✦ Try This: A spherical glass vessel has a cylindrical neck which is 4 cm long and 2 cm in diameter. The diameter of the spherical part is 6 cm. Find the amount of water it can hold?

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 13

NCERT Exemplar Class 9 Maths Exercise 13.4 Problem 7

A sphere and a right circular cylinder of the same radius have equal volumes. By what percentage does the diameter of the cylinder exceed its height?

Summary:

A sphere and a right circular cylinder of the same radius have equal volumes. The diameter of the cylinder exceed its height by 50%

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