Two cans have the same height equal to 21 cm. One can is cylindrical, the diameter of whose base is 10 cm. The other can has square base of side 10 cm. What is the difference in their capacities?

### Concept & Prism Volume Capacity means volume. Both cans are forms of uniform prisms. Volume of any uniform prism = Area of base $\times$ Height. Cylinder Volume: $$\pi r^2 h$$ Square Prism (Cuboid) Volume: $$a^2 h$$ ### Step-by-Step Solution * **Given:** Height ($h$) = 21 cm for both. Cylinder diameter = 10 cm (so $r$ = 5 cm). Square base side ($a$) = 10 cm. * Calculate the capacity of the square can: $$V_{\text{square}} = 10 \times 10 \times 21 = 100 \times 21 = 2100 \text{ cm}^3$$ * Calculate the capacity of the cylindrical can: $$V_{\text{cylinder}} = \frac{22}{7} \times 5^2 \times 21$$ $$V_{\text{cylinder}} = 22 \times 25 \times 3$$ $$V_{\text{cylinder}} = 66 \times 25 = 1650 \text{ cm}^3$$ * Find the difference: $$\text{Difference} = V_{\text{square}} - V_{\text{cylinder}}$$ $$\text{Difference} = 2100 - 1650 = 450 \text{ cm}^3$$ ### Exam Strategy & Shortcut Since height is common, difference in volume = $(\text{Area}_{\text{square\_base}} - \text{Area}_{\text{circle\_base}}) \times \text{height}$. Difference = $(100 - \frac{22}{7} \times 25) \times 21$. Distribute the 21: $2100 - (22 \times 25 \times 3) = 2100 - 1650 = 450$. ### Common Pitfall A frequent error is using the diameter (10) instead of the radius (5) for the cylinder's volume, resulting in an incorrectly massive cylindrical capacity. ### Final Answer Therefore, the correct answer is **450 cm$^3**.