Volume - high school - practice problems - page 8 of 21
Number of problems found: 411
- The ball
The ball has a radius of 2m. What percentage of the surface and volume is another sphere whose radius is 20% larger? - Quadrilateral 15023
The regular quadrilateral pyramid has a base circumference of 44 cm and a body height of 3.2 cm. Calculate its volume and surface. - Conical bottle
When a conical bottle rests on its flat base, the water in the bottle is 8 cm from its vertex. When the same conical bottle is turned upside down, the water level is 2 cm from its base. What is the height of the bottle? - Axial section of the cone
The axial section of the cone is an isosceles triangle in which the ratio of cone diameter to cone side is 2:3. Calculate its volume if you know its area is 314 cm square. - Cone side
Calculate the volume and area of the cone whose height is 10 cm, and the axial section of the cone has an angle of 30 degrees between height and the cone side. - Pool
How many hl of water is in a cuboid pool (a = 25m, b = 8m) if the area of the wetted walls is 279.2 m²? - Octagonal pyramid
Find the volume of a regular octagonal pyramid with height v = 100 and the angle of the side edge with the base plane is α = 60°. - Tetrahedral pyramid
Determine the surface of a regular tetrahedral pyramid when its volume is V = 120 and the angle of the sidewall with the base plane is α = 42° 30'. - Uboid volume
Calculate the cuboid volume if the walls are 30cm², 35cm², 42cm² - Quadrilateral 13881
Please calculate the volume of a quadrilateral pyramid when a = 5cm and the wall height is w = 12cm. - The parabolic segment
The parabolic segment has a base a = 4 cm and a height v = 6 cm. Calculate the volume of the body that results from the rotation of this segment a) around its base b) around its axis. - Cube construction
A 2×2×2 cube will be constructed using four white and four black unit cube. How many different cubes can be constructed in this way? ( Two cubes are not different if one can be obtained by rotating the other. ) - Heptagonal pyramid
A hardwood for a column is in the form of a frustum of a regular heptagonal pyramid. The lower base edge is 18 cm, and the upper base of 14 cm. The altitude is 30 cm. Determine the weight in kg if the wood density is 10 grams/cm³. - The hemisphere
The hemisphere container is filled with water. What is the radius of the container when 10 liters of water pour from it when tilted 30 degrees? - Frustum of a cone
A reservoir contains 28.54 m³ of water when complete. The diameter of the upper base is 3.5 m, while the lower base is 2.5 m. Find the height if the reservoir is in the form of a frustum of a right circular cone. - Cylinder and its circumference
The height of a cylinder is four times its circumference, c. What is the volume of the cylinder in terms of its circumference c? - Secret treasure
Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base of 4 m and a height of 3 m. Find the container's radius r (and height h) so that they can hide the largest possible treasure. - The plaster cast
The plaster cast has the shape of a regular quadrilateral pyramid. The cover consists of four equilateral triangles with a 5 m side. Calculate its volume and surface area. - Faces diagonals
If a cuboid's diagonals are x, y, and z (wall diagonals or three faces), find the cuboid volume. Solve for x=1.3, y=1, z=1.2 - Tetrahedral pyramid
A regular tetrahedral pyramid is given. Base edge length a = 6.5 cm, side edge s = 7.5 cm. Calculate the volume and the area of its face (side area).
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