1.A carpet was ordered with its length and width in the ratio 3:2. Later, the dimensions were changed so that the length and width were in the ratio 7:3, while the perimeter remained unchanged. What is the ratio of the areas of the carpet before and after the modification?
2.A circle has a radius of 21 cm and a central angle measuring 135°. What is the perimeter of the corresponding sector?
3.A rectangle's length is two-fifths of the radius of a circle. The radius of this circle is equal to the side length of a square whose area measures 1225 square units. If the rectangle's breadth is 10 units, what is its area in square units?
4.Calculate the area of a rhombus with each side measuring 25 cm and one diagonal equal to 30 cm.
5.If the volumes of two cubes are in the ratio 729 to 1331, what is the ratio of their total surface areas?
6.A metal sphere with a radius of 12 cm is melted and reshaped into a cylindrical wire having a cross-sectional radius of 16 cm. What is the length of this wire?
7.Two cones have their volumes in the ratio 1 to 10, while their radii are in the ratio 1 to 2. What is the ratio of their heights?
8.A wheel has a radius of 22.4 cm. How far will the wheel travel after completing 500 full rotations?
9.A room measures 25 feet in length, 15 feet in width, and 12 feet in height. If the cost to whitewash the four walls is Rs. 5 per square foot, what will be the total expense given that the room has one door measuring 6 feet by 3 feet and three windows each measuring 4 feet by 3 feet?
10.A cube with an edge length of 1 meter is divided into smaller cubes, each with an edge length of 10 centimeters. How many smaller cubes are formed?
11.Two circles have different radii. The area of a square is 196 cm², and its side length is half the radius of the larger circle. If the radius of the smaller circle is three-sevenths of the radius of the larger circle, what is the circumference of the smaller circle?
12.The perimeter of a square is the same as the perimeter of a rectangle measuring 16 cm in length and 14 cm in width. Calculate the circumference of a semicircle whose diameter equals the side length of the square. (Round your answer to two decimal places.)
13.A circular garden has a diameter of 4 meters, and a 25 cm wide path is to be constructed all around it. What is the approximate area of this path in square meters?
14.Two circles have circumferences measuring 264 meters and 352 meters respectively. Calculate the difference in their areas between the larger and the smaller circle.
15.The perimeter of a square is twice the perimeter of a rectangle. Given that the rectangle's area is 480 square centimeters, determine the area of the square.
16.A square has an area of 4096 square centimeters. If a rectangle's length is twice the side length of this square and its breadth is 24 cm shorter than the square's side, what is the ratio of the rectangle's breadth to its length?
17.A wire is initially shaped as a circle with a radius of 3.5 meters. It is then reshaped into a rectangle where the length and width maintain a ratio of 6 to 5. What is the area of this rectangle?
18.A square's area is five times larger than the area of a rectangle measuring 125 cm by 64 cm. What is the perimeter of the square?
19.Calculate the total expense to construct a fence around a square plot whose area is 289 square feet, given that the fencing costs Rs. 58 per foot.
20.A carpet was ordered with a width of 6 meters and a length that is 1.44 times its width. If another carpet has its length increased by 40% and its width increased by 25% compared to the original, what is the cost of this larger carpet given that the price is Rs. 45 per square meter?