CBSE Class 10 Mathematics Basic 2024: question 32(b)

Hints

Open one hint at a time and try again before the next.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

1. Radius of hemisphere = radius of cone $=r=\frac{7}{2}$ cm.

   1 mark

2. Height of cone $h=r=\frac{7}{2}$ cm.

   ½ mark

3. Volume of solid = volume of hemisphere + volume of cone $=\frac{2}{3}\pi r^3+\frac{1}{3}\pi r^{2}h=\frac{1}{3}\pi r^2(2r+h)$

   1½ marks

4. $=\frac{1}{3}\times \frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}\times \left(2\times \frac{7}{2}+\frac{7}{2}\right)=\frac{1}{3}\times \frac{77}{2}\times \frac{21}{2}$

   1½ marks

5. $=\frac{539}{4}=134.75{\text{cm}}^3$

   ½ mark

Answer: Volume = 539/4 cm³ = 134.75 cm³

Revise the chapter

• Chapter: Surface Areas and Volumes (notes, formulas, where marks are lost and every past question)
• Topic: Volume of a Combination of Solids