1. If each edge of a cube is increased by 10%, by what percentage will its total surface area increase?

(a) 10% (b) 20% (c) 21% (d) 23%

2. If each edge of a cube is increased by 10%, by what percentage does the total surface area increase?

(a) 30.2% (b) 39.6% (c) 33.1% (d) 38.3%

3. If the length of each edge of a cube is doubled, then by what percentage will the total surface area of the cube increase?

4. Let the length of each edge of the cube be \(a\) cm \(\therefore\) The total surface area of the cube = \(6a^2\) square cm If the edge length is increased by 20%, the new edge length = \(a + a \times \cfrac{20}{100}\) cm \(= a + \cfrac{a}{5} = \cfrac{6a}{5}\) cm \(\therefore\) New total surface area of the cube = \(6\left(\cfrac{6a}{5}\right)^2\) square cm = \(\cfrac{216a^2}{25}\) square cm \(\therefore\) Percentage increase in surface area \(= \cfrac{\cfrac{216a^2}{25} - 6a^2}{6a^2} \times 100\%\) \(= \cfrac{(216a^2 - 150a^2) \times 100}{25 \times 6a^2}\%\) \(= \cfrac{4 \times 66a^2}{6a^2}\%\) \(= 44\%\)

5. If each edge of a cube increases by 10%, by what percentage will the total surface area increase?

(a) \(10\%\) (b) \(20\%\) (c) \(21\%\) (d) \(41\%\)

6. If the length of each edge of a cube increases by 50%, by what percentage will the total surface area of the cube increase?

7. If the length of each edge of a cube is increased by 50%, by what percentage will its volume increase?

8. If each edge of a cube decreases by 10%, by what percentage will the total surface area decrease?

(a) \(10\%\) (b) \(17\%\) (c) \(21\%\) (d) \(19\%\)

9. If each edge of a cube is increased by 50%, calculate the percentage increase in its total surface area.

10. If the radius of a sphere is increased by 3%, by what percentage will its surface area increase?

(a) 6.09% (b) 7% (c) 5.06% (d) 9%

11. If the radius of a sphere is increased by 50%, by what percentage will its curved surface area increase?

12. If each side of a square is increased by 10%, by what percentage will its area increase?

13. If each edge of a cube is decreased by 10%, what is the percentage decrease in its total volume?

(a) 36.2% (b) 27.1% (c) 30.5% (d) 20.6%

14. If the radius of a right circular cone is kept constant and its height is increased by 10%, by what percentage will the volume increase?

(a) 10% (b) 11% (c) 12% (d) 14%

15. If the radius of a sphere is increased by 50%, write what percentage increase occurs in its curved surface area.

16. If the radius of a sphere is doubled, by what percentage does its curved surface area increase?

17. If the radius of a sphere is increased by 2 cm, its curved surface area increases by 352 square centimeters. What was the original radius of the sphere?

(a) 5 cm (b) 6 cm (c) 7 cm (d) 5.6 cm

18. If the length of a cuboid is increased by 10%, the width by 20%, and the height is decreased by 30%, what is the percentage change in its volume?

(a) 6.5 increased (b) 7.6 increased (c) 6.5decreased (d) 7.6 decreased

19. The curved surface area of a sphere decreases from \(16\pi\) square centimeters to \(4\pi\) square centimeters. By what percentage will the volume of the sphere decrease?

20. If the ratio of the volumes of two cubes is 8:27, then what will be the ratio of their total surface areas?

21. Each edge of a cube is reduced by 50%. What is the ratio of the volume of the original cube to that of the reduced cube?

22. From a cuboid measuring 16 cm × 4 cm × 2 cm, several cubes with edge length 2 cm are cut out. What is the ratio of the total surface area of the original cuboid to the total surface area of all the cubes?

(a) 11:48 (b) 12:50 (c) 13:36 (d) 14:28

23. If the length of the diagonal of each face of a cube is \(6\sqrt{2}\) cm, what is the total surface area of the cube?

24. Two cubes with equal edge lengths are joined side by side to form a cuboid. If the volume of the cuboid is 1024 cubic centimeters, what is the length of each edge of the cubes?

25. Each edge length of a cube is increased by 25%. Determine the ratio of the volume of the original cube to the volume of the modified cube.

26. Determine the percentage increase in the surface area of a sphere when its radius is increased by 25%.

27. Here's the English translation: **"If the radius of a right circular cone is kept unchanged but its height is doubled, by what percentage will its volume increase?"** Let me know if you'd also like help solving it!

28. The radius of a right circular cylinder is decreased by 50% and the height is increased by 50%. What will be the percentage change in the volume of the cylinder?