1.A river with a depth of 2 meters and a width of 45 meters flows at a speed of 3 km/h. How much water, in cubic meters, passes into the sea every minute?
2.An open box has external dimensions of 52 cm by 40 cm by 29 cm, with a wall thickness of 2 cm. If each cubic centimeter of the metal used weighs 0.5 grams, what is the total weight of the box?
3.What is the ratio of the volume of a cube to the volume of the largest sphere that can fit inside it?
4.A room measures 15 meters in length, 4 meters in width, and 3 meters in height. Calculate the expense of whitewashing all four walls if the rate is 50 paise per square meter.
5.What length of carpet, 50 cm in width, is needed to cover a floor measuring 30 meters by 20 meters?
6.A rectangular courtyard has its length and width in the ratio 4:3. If the total cost to pave the courtyard is Rs. 600 at a rate of 50 paise per square meter, what is the length of the courtyard's diagonal?
7.Given two cubes with side lengths in the ratio 4:3, what is the ratio of their space diagonals?
8.Three metal cubes with edge lengths of 9 cm, 12 cm, and 15 cm are melted and recast into a single cube. What is the edge length of the new cube?
9.If the radii of two spheres are in the ratio 1 to 3, what is the ratio of their volumes?
10.From a sphere with a radius of 3 cm, how many smaller spheres each with a radius of 1 cm can be formed?
11.What is the ratio of the total surface area of a sphere to that of a hemisphere?
12.The curved surface area of a sphere measures 64π cm². What is the radius of the sphere?
13.A cone has a slant height of 12 cm and a base radius of 4 cm. What is the area of its curved surface?
14.A cone has a base area measuring 30 cm² and a height of 6 cm. What is the volume of the cone?
15.A cone has a base radius of 3 cm and a height of 4 cm. What is the volume of this cone?
16.What is the ratio of the curved surface areas of two cylinders with equal heights if their radii are in the ratio 1:2?
17.Two cylinders have equal heights, and their radii are in the ratio 1:3. If the volume of the smaller cylinder is 40 cubic centimeters, what is the volume of the larger cylinder?
18.Calculate the cost of excavating a well that is 14 meters deep with a diameter of 3 meters, if the rate is Rs.15 per cubic meter.
19.A cylinder has a radius of 7 cm and a height of 3 cm. What is the total surface area of this cylinder?
20.A cylindrical container has a diameter of 6 cm and a height of 5 cm. What is the volume of this cylinder?