Question

A solid oblique cone with a slant length of 17 units is placed inside an empty cylinder with a congruent base of radius 8 units and a height of 15 units. A solid oblique cone with a slant length of 17 units is inside an empty cylinder with a congruent base of radius 8 units and a height of 15 units. What is the unfilled volume inside the cylinder? 320π cubic units 597π cubic units 640π cubic units 725π cubic units asap pls​

Answer 1

Correct question :-

A solid oblique cone with a slant length of 17 units is inside an empty cylinder with a congruent base of radius 8 units and a height of 15 units. What is the unfilled volume inside the cylinder?

Options:-

a) 320π cubic unit

b) 597π cubic unit

c) 640π cubic unit

d) 725π cubic unit

Given :-

• Slant height of cone = 17 units

• Base radius of cylinder = 8 units

• Height of cylinder = 15 units

To Find :-

• What's the unfilled volume inside the given cylinder?

Formula to be used :-

• Slant height , l² = √r²+ h²

•Volume of cylinder = πr²h

•Volume of cone = ⅓ πr²h'

Solution :-

Firstly, we need to find the height of the given cone.

We know,

Slant height , l² = √r²+ h²

Given that,

Slant height = 17 unit

Radius of cone = 8 unit = Radius of cylinder

Now,

⟼ l² = √r²+ h²

⟼ 17² = 8² + h²

⟼ 238 = 64 + h²

⟼ 238 - 64 = h²

⟼ √225 = h

⟼ h = 15

Hence, height of the cone is = 15 unit

Again,

_________________________________________

Volume of cylinder = πr²h

Put the given values in the formula

Volume of cylinder = πr²h

⟼Volume of cylinder = π × ( 8)² × 15

$⟼volume \: of \: cylinder \: = 960\pi$

__________

Volume of cone = ⅓ πr²h'

⟼ Volume of cone = ⅓ × π × ( 8)² × h'

⟼ Volume of cone = 320π cubic unit

Hence,

Unfilled volume inside the cylinder

= Volume of cylinder - volume of cone

= 960π - 320π

= 640π cubic unit

Unfilled volume of cylinder is = 640π cubic unit

Therefore, option ( c) is correct.