Question

a sphere is a right circular cylinder of the same radius have equal volumes. what percentage does the diameter of the cylinder exceed its height​

Answer 1

✬ Percentage = 50% ✬

Step-by-step explanation:

Given:

• A sphere and a right cylinder have same same radius and also their volumes are equal.

To Find:

• What percentage does the diameter of cylinder exceed its height ?

Solution: Let the height be 100% .

As we know that

★ Volume of Sphere = 4/3πr³ ★

★ Volume of Cylinder = πr²h ★

Now, a/q

• Vol. sphere = Vol. cylinder

$\implies{\rm }$ 4/3πr³ = πr²h

$\implies{\rm }$ 4/3(r³) = r²h

$\implies{\rm }$ 4/3(r) = h

$\implies{\rm }$ 4r = 3h

$\implies{\rm }$ 2(2r) = 3h

$\implies{\rm }$ 2r = 3h/2

$\implies{\rm }$ d = 3h/2

[ Height is 100% then ]

➟ d = 3(100%)/2

➟ d = 300%/2

➟ d = 150%

Hence, the difference will be

=> (150 – 100)%

=> 50%

Hence, the diameter of the cylinder exceed its height by 50%.

Answer 2

✬ Percentage = 50% ✬

Step-by-step explanation:

Given:

A sphere and a right cylinder have same same radius and also their volumes are equal.

To Find:

What percentage does the diameter of cylinder exceed its height ?

Solution: Let the height be 100% .

As we know that

★ Volume of Sphere = 4/3πr³ ★

★ Volume of Cylinder = πr²h ★

Now, a/q

Vol. sphere = Vol. cylinder

⟹ 4/3πr³ = πr²h

⟹ 4/3(r³) = r²h

⟹ 4/3(r) = h

⟹ 4r = 3h

⟹ 2(2r) = 3h

⟹ 2r = 3h/2

⟹ d = 3h/2

[ Height is 100% then ]

➟ d = 3(100%)/2

➟ d = 300%/2

➟ d = 150%

Hence, the difference will be

=> (150 – 100)%

=> 50%

Hence, the diameter of the cylinder exceed its height by 50%.