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NCERT Exemplar Solutions Class 10 Mathematics Solutions for Surface Areas and Volumes - Exercise 12.4 in Chapter 12 - Surface Areas and Volumes

Question 5 Surface Areas and Volumes - Exercise 12.4

A hemispherical bowl of internal radius 9 cm is full of liquid. The liquid is to be filled into cylindrical shaped bottles each of radius 1.5 cm and height 4 cm. How many bottles are needed to empty the bowl?

Answer:

n cylindrical bottle Hemisphere
r = 1.5 cm R = 9 cm
R = 9 cm

As the volume of liquid does not change

So, Volume of n bottles = Volume of hemisphere

\Rightarrow \mathrm{n} \pi \mathrm{r}^{2} \mathrm{~h}=\frac{2}{3} \pi \mathrm{R}^{3} \\ \Rightarrow \mathrm{nr}^{2} \mathrm{~h}=\frac{2}{3} \mathrm{R}^{3} \\ \Rightarrow \mathrm{n} \times 1.5 \times 1.5 \times 4=\frac{2}{3} \times 9 \times 9 \times 9 \\ \Rightarrow \mathrm{n}=\frac{2 \times 9 \times 9 \times 9 \times 100}{3 \times 15 \times 15 \times 4}=54

Hence, 54 bottles are needed.

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