1.What is the volume of soil removed when excavating a pond measuring 20 meters in length, 10 meters in width, and 5 meters in depth?
2.If the height of a cone is doubled, by what percentage does its volume increase?
3.A cone and a cylinder share the same base radius and height. What is the ratio of the volume of the cylinder to the volume of the cone?
4.What is the maximum length of a rod that can be placed inside a cube-shaped room with each side measuring 4 meters?
5.What is the total surface area in square centimeters of a cardboard box measuring 25 cm by 15 cm by 8 cm?
6.A rectangular tank measuring 3 meters in length, 2 meters in width, and 1.5 meters in depth is excavated in a field that is 20 meters long and 14 meters wide. If the soil removed from the tank is uniformly spread over the entire field, by approximately how many centimeters will the field's surface level rise?
7.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?
8.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?
9.What is the ratio of the volume of a cube to the volume of the largest sphere that can fit inside it?
10.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.
11.What length of carpet, 50 cm in width, is needed to cover a floor measuring 30 meters by 20 meters?
12.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?
13.Given two cubes with side lengths in the ratio 4:3, what is the ratio of their space diagonals?
14.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?
15.If the radii of two spheres are in the ratio 1 to 3, what is the ratio of their volumes?
16.From a sphere with a radius of 3 cm, how many smaller spheres each with a radius of 1 cm can be formed?
17.What is the ratio of the total surface area of a sphere to that of a hemisphere?
18.The curved surface area of a sphere measures 64π cm². What is the radius of the sphere?
19.A cone has a slant height of 12 cm and a base radius of 4 cm. What is the area of its curved surface?
20.A cone has a base area measuring 30 cm² and a height of 6 cm. What is the volume of the cone?