# Pythagorean theorem + volume - math problems

#### Number of problems found: 153

• 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/cm ^ 3
• 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.
• 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.
• Axial section Calculate the volume and surface of a cone whose axial section is an equilateral triangle with side length a = 18cm.
• 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 the surface area and volume of a regular tetrahedron 4.9 cm high, the base edge has a length of 6 cm.
• 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.
• Surface and volume - cube Find the surface and volume of a cube whose wall diagonal is 5 cm long.
• The volume The volume of the cone is 94.2dm³, the radius of the base is 6 dm Calculate the surface of the cone.
• Truncated pyramid Find the volume and surface area of a regular quadrilateral truncated pyramid if base lengths a1 = 17 cm, a2 = 5 cm, height v = 8 cm.
• 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.
• Truncated cone Find the volume and surface area of the truncated cone if r1 = 12 cm, r2 = 5 cm and side s = 10 cm.
• Isosceles + prism Calculate the volume of the perpendicular prism if its height is 17.5 cm and the base is an isosceles triangle with a base length of 5.8 cm and an arm length of 3.7 cm
• The base 2 The base diameter of a right cone is 16cm and it's slant height is 12cm. A. ) Find the perpendicular height of the cone to 1 decimal place. B. ) Find the volume of the cone, convert to 3 significant figure. Take pi =3.14
• The cone - S,V Calculate the volume and surface area of the cone if its radius r = 6 cm and side s = 10 cm.
• Průměr kužele Vypočtěte povrch a objem rotačního kužele jehož průměr je 60mm a délka strany 3.4 cm.
• Iglu - cone tent The cone-shaped tent is 3 m high, the diameter of its base is 3.2 m. a) The tent is made of two layers of material. How many m2 of fabric is needed for production (including flooring) if 20% needs to be added to the minimum amount due to cutting waste? b)
• Triangular pyramid Calculate the volume of a regular triangular pyramid with edge length a = 12cm and pyramid height v = 20cm.

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Tip: Our volume units converter will help you with the conversion of volume units. Pythagorean theorem is the base for the right triangle calculator. Pythagorean theorem - math problems. Volume - math problems.