1. The length of a rectangular field is 36 meters more than its breadth. The area of the field is 460 square meters. Form a quadratic equation in one variable from this statement and determine the coefficients of \(x^2\), \(x\), and \(x^0\).

2. The sum of the length, breadth, and height of a rectangular box is 24 cm, and the length of its diagonal is 15 cm. What is the total surface area of the box?

3. The length of the diagonal of a rectangular field is 15 meters, and its length is 3 meters more than its breadth. — Form a quadratic equation with one variable from the given statement.

4. The diagonal of a rectangular field is 15 meters and its length is 3 meters more than its breadth.

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. The sum of the length, width, and height of a rectangular box is 24 cm, and the length of its diagonal is 15 cm. What is the total surface area of the rectangular box?

(a) 360 square cm (b) 221 square cm (c) 351quare cm (d) 256 quare cm

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

8. Here’s the English translation of your sentence: "A right rectangular prism has its length twice the breadth and its height half the breadth. If the total surface area of the prism is 448 square centimeters, find its volume."

9. If the diagonal of a rectangle is 10 cm and its area is 62.5 square cm, then the sum of the length and breadth of the rectangle is —

(a) 12 cm (b) 15 cm (c) 20 cm (d) 25 cm

10. The area of a trapezium-shaped field is 162 square centimeters and its height is 6 cm. If one of the parallel sides of the trapezium is 23 cm long, then the length of the other parallel side is –

(a) 29 cm (b) 31 cm (c) 32 cm (d) 33 cm

11. The rectangular village field has a length of 20 meters and a width of 15 meters. To install pillars at the four corners, four cube-shaped holes of 4 meters in length were dug and the removed soil was spread evenly over the remaining area of the field. Calculate how much the surface level of the field will rise.

12. The sum of the length, width, and height of a right rectangular prism is 25 cm, and its total surface area is 264 square cm. Determine the length of its diagonal.

13. "A team of firefighters used a water-filled cylindrical tanker to extinguish a fire by spraying water through three hosepipes, each with a diameter of 2 cm, at a rate of 420 metres per minute for 40 minutes. If the diameter of the tanker is 2.8 metres and its length is 6 metres, then (i) calculate how much water was used to extinguish the fire, and (ii) determine how much water remains in the tanker."

14. The length of a right rectangular prism is three times its width and five times its height. If its volume is 14,400 cubic centimeters, then what is its total surface area?

(a) 4300 square cm (b) 4320 square cm (c) 4500 square cm (d) 4520 square cm

15. 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

16. 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

17. 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

18. The diagonal of a cuboid is √725 cm and its volume is 3000 cubic cm. The total surface area of the cuboid is 1300 square cm. Find the length, breadth, and height of the cuboid.

19. In the adjacent figure, BX and CY are the bisectors of ∠ABC and ∠ACB respectively. Given that AB = AC and BY = 4 cm, find the length of AX.

(a) 4 cm (b) 8 cm (c) 6 cm (d) 10 cm

20. The length of the diagonal of a rectangular field is 15 meters, and its length is 3 meters more than its width. What is the length of the rectangular field?

(a) 9 meter (b) 12 meter (c) 15 meter (d) 18 meter

21. The area of a rectangular park is 600 square meters and its perimeter is 100 meters. Find the length and breadth of the park.

22. "The differences between the semi-perimeter of a triangle and the lengths of its sides are respectively 4 cm, 7 cm, and 5 cm. The area of the triangle is –"

(a) \(20\sqrt{7}\) square cm (b) \(10\sqrt{14}\) square cm (c) \(20\sqrt{14}\) square cm (d) 140 square cm

23. If the length of one diagonal of a rhombus is three times the length of the other diagonal, and the area of the rhombus-shaped field is 96 square centimeters, then the length of the longer diagonal is –

(a) 8 cm (b) 12 cm (c) 16 cm (d) 24cm

24. A rectangular box has its length, breadth, and height in the ratio 3:2:1, and its volume is 384 cubic centimeters. Find the surface area of the box.

25. In a rectangular prism, the ratio of length, width, and height is \(4:5:3\). If the length of one diagonal is \(35\sqrt2\) cm, what is the total surface area?

26. A rectangular sheet of paper has a length of \(l\) units and a breadth of \(b\) units. The sheet is rolled to form a right circular cylinder, where the circumference equals the length of the paper. The curved surface area of the cylinder is ____ square units.

27. If the length, breadth, and height of a rectangular box are in the ratio 3:2:1 and its volume is 384 cubic centimeters, calculate and write the total surface area of the box.

28. The rectangular village field has a length and breadth of 20 meters and 15 meters respectively. To install pillars at each corner, four cube-shaped pits of 4 meters in length were dug, and the excavated soil was spread evenly over the remaining area of the field. Calculate and write how much the ground level of the remaining field rose.

29. A rectangular pond is 20 meters long and 18.5 meters wide, and contains water to a depth of 3.2 meters. A pump that can irrigate 160 kiloliters of water per hour is used to remove all the water from the pond. Calculate and write how long it will take to pump out all the water. If this water is then used to irrigate a field with embankments measuring 59.2 meters in length and 40 meters in width, calculate and write the depth of water that would cover the field. [Note: 1 cubic meter = 1 kiloliter]

30. The length of a rectangular sheet of paper is \(l\) units and its breadth is \(b\) units. The paper is rolled to form a right circular cylinder such that the circumference of the base is equal to the length of the paper. The curved surface area of the cylinder is ____________ square units.