Volume + Pythagorean theorem - practice problems
Number of problems found: 289
- Cuboid - sum of edges length
Calculate the cuboid's dimensions if the sum of its edges is 19 cm. The body's diagonal size is 13 cm, and its volume is 144 cm³. The total surface area is 192 cm². - A frustum
A frustum of a pyramid consists of a square base of length 10 cm and a top square of length 7 cm. The height of the frustum is 6 cm. Calculate the surface area and volume. - Spherical 83427
The bowl, in the shape of part of a spherical surface, has a diameter of 28 cm at the top edge and is 8 cm deep. What is the total volume of the bowl? How much water would you have to pour into the bowl to fill it halfway? - Quadrilateral pyramid
The volume of a regular quadrilateral pyramid is 72 cm³. Its height is equal to the length of the base edge. Calculate the length of the base and the surface of the pyramid.
- Equilateral 83322 The glass weight has the shape of a regular four-sided pyramid with a base edge of 10 cm. The shell walls are equilateral triangles. What is the weight in grams of the paperweight if the density of the glass is 2500kg/m³?
- Quadrilateral 83307
The diagonal of section DBFH of the regular quadrilateral prism ABCDEFGH inscribes a circle with a diameter of 8 cm. What is the volume of the prism? - Quadrilateral 83272 Calculate the surface area and volume of a regular quadrilateral pyramid whose base edge is 5 cm long and whose height is 10 cm.
- Quadrilateral 83254 What is the volume of a regular quadrilateral pyramid if its base edge a = √18 cm and side edge b = 5 cm?
- Calculate 83044
The cube comprises 64 small cubes, each with an edge length of 15 mm. Calculate the wall length and body diagonals.
- Calculate 82700
A cone of rotation with a radius of 32 cm and side length s = 65 cm is given. Calculate the surface area and volume. - Calculate 82690
A cone of rotation with a height of 18 cm and side length s = 45 cm is given. Calculate the surface area and volume. - Calculate 82567
The volume of a cuboid with a square base is 64 cm3, and the body diagonal deviation from the base's plane is 45 degrees. Calculate its surface area. - Diagonal of a cube
Calculate the volume of a cube with a wall diagonal of u = 20 cm. - Right-angled 82416
What are the sides of a right-angled triangle with a perimeter of 45 centimeters and a volume of 67.5 cm²?
- Quadrilateral 82146 Calculate the volume and surface area of a regular quadrilateral prism with base edge a=24 cm if the body diagonal makes an angle of 66° with the base.
- Calculate 82073 Calculate a cone's volume and surface area with base diameter d = 22 cm and body height v = 40 cm.
- Quadrilateral 82066 Calculate the volume of a regular quadrilateral pyramid with a square base of side a = 3 cm and side length b = 7 cm.
- Inscribed 81949
A cube is inscribed in a sphere with a radius of 27 cm. Calculate its volume and surface area. - Cantilevers 81937 Calculate a prism's volume and surface area with a base of a right triangle with cantilevers of length 40 and 43 cm. The height of the prism is 60 cm.
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