1. Similar shapes have length scale factor 4. A smaller length is 3 cm. Find the matching larger length.

Answer: 12 cm.

2. Similar shapes have length scale factor 3. The smaller area is 8 cm$^2$. Find the larger area.

Answer: 72 cm$^2$.

3. Similar solids have length scale factor 2. The smaller volume is 15 cm$^3$. Find the larger volume.

Answer: 120 cm$^3$.

4. Similar rectangles have lengths 6 cm and 15 cm. The smaller area is 24 cm$^2$. Find the larger area.

Answer: 150 cm$^2$.

5. Similar solids have corresponding lengths 4 cm and 10 cm. The smaller volume is 32 cm$^3$. Find the larger volume.

Answer: 500 cm$^3$.

6. Similar shapes have area scale factor 25. Find the length scale factor.

Answer: The length scale factor is $5$ (since $5^2=25$).

7. Similar shapes have length scale factor 4 from small to large. The large area is 400 cm$^2$. Find the small area.

Answer: 25 cm$^2$.

8. Similar solids have length scale factor 3 from small to large. The large volume is 540 cm$^3$. Find the small volume.

Answer: 20 cm$^3$.

9. A cuboid is enlarged by scale factor 1.5. Original volume is 80 cm$^3$. Find the new volume.

Answer: 270 cm$^3$.

10. Similar triangles have side ratio small:large $2:5$. Find the area ratio.

Answer: Area ratio small:large is $4:25$.

11. A similar shape has area scale factor 9. Its original corresponding length is 7 cm. Find the enlarged length.

Answer: 21 cm.

12. Similar objects have volume ratio small:large $8:125$. Find the length ratio small:large.

Answer: Length ratio small:large is $2:5$.

13. A similar shape has length scale factor 3. A matching length is 4 cm and a smaller area is 7 cm$^2$. Work out the enlarged length and area. Choose the factor for each quantity and explain why they differ.

Answer: The enlarged length is 12 cm. The enlarged area is 63 cm$^2$. Lengths use a factor of 3; areas use $3^2=9$.