Question

a hemispherical bowl is completely filled when 9 cups of water poured in it. find the cups is a circular cylinder,whosee height is twic its radius. find the rato of radius of the bowl to the radius of the cups

Answer 1

If the circular cylindrical cups have their height twice its radius then the ratio of radius of the bowl into which the 9 cups of water is poured to the radius of the cups is 3:1.

Step-by-step explanation:

Let the radius of the hemispherical bowl be “R” and the radius of the circular cylindrical cup be “r”.

The height of the cup “h” is given as twice its radius, so h = 2r

Since it is given that the hemispherical bowl is filled with 9 cups of water, therefore we can write  

[The volume of the hemispherical bowl] = 9 × [the volume of circular cylindrical cup]

⇒ ⅔ π R³ = 9 * π * r² * h

⇒ ⅔ * π * R³ = 9 * π * r² * 2r

⇒ R³ = 9 * r²  * 2r * $\frac{3}{2}$

⇒ R³ = r³ × 27

taking cube roots throughout

⇒ R = r * 3

⇒ $\frac{R}{r}$ = $\frac{3}{1}$

Thus, the ratio of the radius of the bowl to the radius of the cups is 3:1.

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