Pythagorean theorem + volume - practice problems - page 6 of 15
Number of problems found: 289
- Pentagonal pyramid
The height of a regular pentagonal pyramid is as long as the edge of the base, 20 cm. Calculate the volume and surface area of the pyramid. - Ratio of edges
The cuboid dimensions are in a ratio of 3:1:2. The body diagonal has a length of 28 cm. Find the volume of a cuboid. - Perpendicular prism network
Find the volume and surface of a triangular prism with the base of a right triangle, the network of which is 4 cm 3 cm (perpendiculars) and nine centimeters (height of the prism). - Ratio-cuboid
The lengths of the edges of the cuboid are in the ratio 2: 3: 6. Its body diagonal is 14 cm long. Calculate the volume and surface area of the cuboid. - Hexagonal prism
The prism's base is a regular hexagon consisting of six triangles with side a = 12 cm and height va = 10.4 cm. The prism height is 5 cm. Find the volume and surface of the prism. - Cone container
The Rotary cone-shaped container has a volume of 1000 cubic cm and a height of 12 cm. Calculate how much metal we need for making this package. - Pyramid 8
Calculate the volume and the surface area of a regular quadrangular pyramid with a base side of 9 cm and a side wall with the base has an angle of 75°. - Calculate 71374
Calculate the volume and surface of a cone whose base diameter is 6 cm and height is 0.9 dm. - Decorative 46721
How many liters of water can fit in a decorative garden tank in the shape of a regular hexagonal pyramid with a 30 cm long base edge? The depth of the tank is 30 cm. - Intersection 40981
The intersection of a plane is 2 cm from the sphere's center, and this sphere is a circle whose radius is 6 cm. Calculate the surface area and volume of the sphere. - Calculate 5789
Calculate the volume and surface of the rotating cone with the base radius r = 4.6dm and the height v = 230mm. - Calculate 4689
The area of the rotating cone shell is 240 cm2, and the area of its base is 160 cm². Calculate the volume of this cone. - Floating barrel
The barrel (cylinder shape) floats on water, the top of the barrel is 8 dm above water, and the width of surfaced barrel part is 23 dm. Barrel length is 24 dm. Calculate the volume of the barrel. - Regular quadrilateral pyramid
Find the surface area of a regular quadrilateral pyramid with a volume of 24 dm³ and a height of 45 cm. - Quadrilateral pyramid,
A quadrilateral pyramid has a rectangular base with 24 cm and 13 cm dimensions. The height of the pyramid is 18cm. Calculate 1/the area of the base 2/casing area 3/pyramid surface 4/volume of the pyramid - 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). - Cube wall
Calculate the cube's diagonal if you know that one wall's surface is equal to 36 centimeters square. Please also calculate its volume. - Body diagonal
The cuboid has a volume of 32 cm³. Its side surface area is double as one of the square bases. What is the length of the body diagonal? - Pyramid in cube
In a cube with an edge 12 dm long, we have an inscribed pyramid with the apex at the center of the cube's upper wall. Calculate the volume and surface area of the pyramid. - Triangular pyramid
It is given perpendicular regular triangular pyramid: base side a = 5 cm, height v = 8 cm, volume V = 28.8 cm³. What is its area (surface area)?
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