Question

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Answer 1

Given:

• A cylinder is within the cube touching all the vertical faces and a cone is inside the cylinder.
• Their heights and radius are same.

Find:

• Ratio of thier volume

Solution:

For Cube:

Length of each edge of cube = a units

we, know that

➺ Volume of cone = a³

➺ V₁ = a³ cubic units

For Cylinder:

Height of cylinder = a units

Radius of cylinder = a/2 units

we, know that

↬ Volume of Cylinder = πr²h

↬ V₂ = 22/7(a/2)²(a)

↬ V₂ = 22/7(a²/4)(a)

↬ V₂ = 22/7(a²/4)(a)

↬ V₂ = 11/7 (a²/2) (a)

↬ V₂ = 11a²/14(a)

↬ V₂ = 11a³/14 cubic units

For Cone:

Height of cone = a units

Radius of cone = a/2 units

we, know that

➲ Volume of cone = 1/3 πr²h

➲ V₃ = 1/3(22/7)(a/2)²(a)

➲ V₃ = 1/3(22/7)(a²/4)(a)

➲ V₃ = (22/21)(a²/4)(a)

➲ V₃ = (11/21)(a²/2)(a)

➲ V₃ = (11a²/42)(a)

➲ V₃ = 11a³/42 cubic units

_____________________________

Ratio of their volumes:

$\sf \dashrightarrow V_1: V_2 :V_3$

$\sf \dashrightarrow {a}^{3} : \frac{11 {a}^{3} }{14} : \frac{11 {a}^{3} }{42}$

$\sf \dashrightarrow 42: 33: 11$

Hence, ratio of their volumes are 42:33:11

Answer 2

Step-by-step explanation:

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