Question

hemispherical bowl of internal diameter 36 CM contains a liquid. This liquid is to be filled in cylindrical bottles of radius 3 cm in height 6 cm how many bottles are required to empty the bowl

Answer 1

hiii!!!

here's Ur answer..

given the radius of the hemispherical bowl = 36cm

therefore volume of the liquid in the hemispherical bowl = 2/3πr³

= 2/3 × 22/7 × 36 × 36 × 36

= 44/7 × 12 × 36 × 36

= 684288/7cm³

given radius of the cylindrical bottle is 3cm and height of the cylindrical bottle is 6cm

volume of the cylindrical bottle = πr²h

= 22/7 × 3 × 3 × 6

= 1188/7cm³

hence, number of cylindrical bottles required to empty the bowl = volume of hemispherical bowl ÷ volume of cylindrical bottle

= 684288/7 × 7/1188

= 684288/1188

= 576

hence, 576 cylindrical bottles are required to empty the hemispherical bowl.

hope this helps..!!

Answer 2

AnswEr:

We have ,

◕ Radius of hemispherical bowl = 18 cm

◕ Volume of hemispherical bowl = $\sf\dfrac{2}{3}\pi\times\:(18)^3\:cm^3$

◕ Radius of cylindrical bottle = 3 cm

◕ Height of a cylindrical bottle = 6 cm

◕ Volume of a cylindrical bottle = $\sf{(\pi\times\:3^2\times\:6)\:cm^3}$

__________________________

Suppose x bottles are required to empty the bowl.

◕ Volume of x cylindrical bottle = $\sf{(\pi\times\:9\times\:6\times\:\pi)cm^3}$

Clearly,

◕ Volume of the liquid in x bottles = Volume of bowl

$\implies \sf\pi \times 9 \times 6 \times x = \dfrac{2\pi}{3} \times (18) {}^{3} \\ \\ \implies \sf \: x = \frac{2\pi \times {18}^{3} }{3 \times \pi \times 9 \times 6} = 72$

Hence, 72 bottles are required to empty the bowl.

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