CBSE Class 10 Mathematics Standard 2023: question 34

Hints

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Step-by-step solution

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1. Radius of the cylinder = radius of each cone: $r=\frac{3}{2}$ cm.

   Height of each cone: $H=2$ cm.

   Height of the cylinder: $h=12-2\times 2=8$ cm.

   1 mark

2. Volume of air = volume of cylinder + volume of 2 cones

   $=\pi r^{2}h+2\times \frac{1}{3}\pi r^{2}H=\pi r^2\left(h+\frac{2}{3}H\right)$

   1½ marks

3. Substitute the values:

   $=\frac{22}{7}\times \frac{3}{2}\times \frac{3}{2}\left(8+\frac{2}{3}\times 2\right)=\frac{22}{7}\times \frac{9}{4}\times \frac{28}{3}$

   1½ marks

4. $=\frac{22\times 9\times 28}{7\times 4\times 3}=66{\text{ cm}}^3$

   So the volume of air in the model is $66{\text{ cm}}^3$.

   1 mark

Answer: $66{\text{ cm}}^3$

Revise the chapter

• Chapter: Surface Areas and Volumes (notes, formulas, where marks are lost and every past question)