1. If the radius of a right circular cone is decreased by 50% and its height is increased by 50%, what is the percentage change in the volume of the cone?

2. 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%

3. The radius of a right circular cone is reduced by 50% and its height is increased by 50%. By what percentage does the volume of the cone change?

4. 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?

5. If the height of a right circular cone remains unchanged and its radius is increased by 1 unit, the volume of the cone becomes four times its original volume. What is the length of the diameter of the cone?

6. 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%

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

8. The diameter of the cross-section of a wire is reduced by 50%. To keep the volume unchanged, by what percentage must the length of the wire be increased?

9. To raise a plot of land measuring 25.5 meters in length and 20.2 meters in width by filling it with soil up to a height of 1.5 meters, a pit is dug in the adjacent plot with dimensions 15.3 meters in length and 10.1 meters in width. What will be the depth of the pit?

(a) 5 meters (b) 10 meters (c) 15 meters (d) 20 meters

10. 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!

11. 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%

12. If each edge of a cube is increased by 20%, by what percentage will the total surface area increase?

(a) 40% (b) 42% (c) 44% (d) 46%

13. 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 \(= \cfrac{\cfrac{216a^2}{25} - 6a^2}{6a^2} \times 100\%\) \(= \cfrac{(216a^2 - 150a^2) \times 100}{25 \times 6a^2}\%\) \(= \cfrac{4 \times 66a^2}{6a^2}\%\) \(= 44\%\)

14. The base length and width of a rectangular reservoir are 15 meters and 12 meters respectively. Water is filled into the reservoir from a nearby pond using a pump. If the pump can fill 36,000 liters of water per hour, then how long will it take for the pump to fill the reservoir up to a height of 7.2 decimeters? [Note: 1 liter = 1 cubic decimeter]

15. The length, width, and height of a cuboidal room are respectively \(a\), \(b\), and \(c\) units, and given that \(a + b + c = 25\) and \(ab + bc + ca = 240.5\), what is the length of the longest rod that can be placed inside the room?

16. The length of a rectangular field is \(\frac{3}{2}\) times its breadth. If the length is reduced by 1200 cm and the breadth is increased by 1200 cm, the field becomes a square. Find the area of the field.

17. A low-lying plot of land measuring 48 meters in length and 31.5 meters in width is to be raised by 6.5 decimeters. To achieve this, a nearby pit measuring 27 meters in length and 18.2 meters in width is dug. What will be the depth of the pit?

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

19. A cuboidal oil tanker measuring 4 meters in length, 2.5 meters in width, and 10 meters in depth is filled with an additional 12,000 liters of oil. By how many decimeters will the oil level rise?

(a) 20 decimeters. (b) 15 decimeters. (c) 12 decimeters. (d) 22 decimeters.

20. 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%

21. In a business, three friends have their capital investment in the ratio 2:3:4. If in the following year they increase their capital by 10%, 15%, and 20%, respectively, in what ratio will the profit be distributed among them at the end of the second year?

(a) 44 : 69 : 96 (b) 69 : 44 : 96 (c) 96 : 69 : 44 (d) 45 : 96 : 63

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

23. When the sun's altitude angle decreases from 60° to 30°, the length of the shadow of a vertical rod increases by 40 meters. What is the height of the rod?

(a) \(10\sqrt3\) meter (b) \(15\sqrt3\) meter (c) \(5\sqrt3\) meter (d) \(20\sqrt3\) meter

24. 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

25. If the length, breadth, and height of a right rectangular prism are in the ratio 3:2:1 and its total surface area is 88 square centimeters, then what is its volume?

(a) 120 cubic cm (b) 64 cubic cm (c) 48 cubic cm (d) 24 cubic cm

26. If the radius of a sphere is decreased by 10%, by what percentage will the volume decrease?

(a) 10% (b) 25% (c) 27.1% (d) 29.7%

27. There is some water in a vertical cylindrical drum. A conical iron piece with a diameter of 2.8 decimeters and a height of 3 decimeters is completely submerged in the water, causing the water level to rise by 0.64 decimeters. What is the diameter of the drum?

28. As the sun's angle of elevation increases from 30° to 60°, the length of the monument's shadow decreases by \(50\sqrt{3}\) meters. What is the height of the monument?

29. A tank measuring 21 decimeters in length, 11 decimeters in width, and 6 decimeters in depth is half-filled with water. If 100 solid spheres, each with a diameter of 21 centimeters, are submerged into the tank, by how many decimeters will the water level rise?

30. The height of a tree increases by 20% every year. If the current height of the tree is 28.8 meters, what was its height 2 years ago?