Question

A cylindrical bottle with radius 15 cm is half filled with water. A circular stone is dropped inside the bottle and the water level rises by 2.5 cm without spilling out. What is the radius of the stone?

Answer 1

Answer:

the radius of the stone is 7.5 cm

Step-by-step explanation:

The volume of the stone equals to the volume of the water displaced.

The volume of the water displaced is given by:

Volume = π × 15² × 2.5 = 562.5π

Now that we have the volume of the stone, we can calculate the radius of the stone.

Since the stone is circular, we will use the formula for calculating the volume of a sphere

Volume of a sphere = 4/3πr³

We have: 562.5π = 4/3πr³

r³ = 562.5 × 3/4

r³ = 421.875

r = ∛421.875 = 7.5 cm

The radius of the stone is 7.5 cm

Answer 2

Step-by-step explanation:

Given A cylindrical bottle with radius 15 cm is half filled with water. A circular stone is dropped inside the bottle and the water level rises by 2.5 cm without spilling out. What is the radius of the stone?

1. We know that volume of stone = 4/3 π r^3 ------------1
2. where r is the radius of stone
3. Volume of displaced water is equal to change in volume occupied.
4. Therefore ΔV = π x 15^2 x 2.5 -------------2
5. Equating 1 and 2 we get
6. 4/3 π r^3 = π x15^2 x 2.5  
7. So r^3 = 15^2 x 5/2 x 3 / 4(by taking 2.5 as 5/2)
8. So r^3 = (15 / 2)^3

Therefore r = 15/2 = 7.5 cm

Reference link will be

https://brainly.in/question/1104709

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