Volume + Pythagorean theorem - practice problems - page 4 of 15
Number of problems found: 289
- School model
The beech school model of a regular quadrilateral pyramid has a base 20 cm long and 24 cm high. Calculate a) the surface of the pyramid in square decimeters, b) the mass of the pyramid in kilograms if the density of the beech is ρ = 0,8 g/cm³ - Right-angled triangle base
Find the volume and surface area of a triangular prism with a right-angled triangle base if the length of the prism base legs are 7.2 cm and 4.7 cm and the height of a prism is 24 cm. - Frustrum - volume, area
Calculate the surface and volume of the truncated cone. The radius of the smaller figure is 4 cm, the height of the cone is 4 cm, and the side of the truncated cone is 5 cm. - 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. - Regular quadrilateral pyramid
Find the surface area of a regular quadrilateral pyramid if for its volume V and body height v and the base edge a applies: V = 2.8 m³, v = 2.1 m - Triangular 46641
The regular triangular pyramid ABCDV has a base edge length of 8 cm and a height of 7 cm. Calculate the pyramid's surface area and volume. - Regular square prism
The volume of a regular square prism is 192 cm³. The size of its base edge and the body height is 1:3. Calculate the surface of the prism. - Quadrilateral 46431
Calculate the volume V and the surface S of a regular quadrilateral pyramid, the base edge and height of which are the same size as the edge of a cube with a volume V1 = 27m3 - Axial section
Calculate the volume and surface of a cone whose axial section is an equilateral triangle with side length a = 18cm. - Quadrilateral 44561
The regular quadrilateral pyramid has a volume of 212 m³ and a base edge a = 7.2 m. Calculate the surface area and height of the pyramid. - Calculate 44541
Calculate the surface and volume of the cone if you know that the base radius r = 5 dm and the side length s = 7 dm. - Metal balls
Four metal balls with a diameter of 5 cm are placed in a measuring cylinder with an inner diameter of 10 cm. What is the smallest water volume to be poured into the cylinder so that all balls are below the water level? - The tetrahedron
Calculate a regular tetrahedron's surface area and volume 4.9 cm high, and the base edge has a length of 6 cm. - Pyramidal 44061
A pyramidal candle with a square base has a side edge of s = 12 cm and a base edge of 4 cm. How much wax will we need to make it, and how long is the wick if it is 5% bigger than its height? - Base diagonal
In a regular 4-sided pyramid, the side edge forms an angle of 55° with the base's diagonal. The length of the side edge is eight meters. Calculate the surface area and volume of the pyramid. - Side edges
The regular 4-sided pyramid has a body height of 2 dm, and the opposite side edges form an angle of 70°. Calculate the surface area and volume of the pyramid. - 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. - Surface and volume - cube
Find the surface and volume of a cube whose wall diagonal is 5 cm long. - Quadrilateral 40551
Find the volume and surface area of a regular quadrilateral pyramid ABCDV if its leading edge has a length a = 10 cm and a body height h = 12 cm. - The volume
The volume of the cone is 94.2 dm³, and the radius of the base is 6 dm. Calculate the surface of the cone.
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