# Volume + cosine - math problems

#### Number of problems found: 11

• Sphere in cone A sphere of radius 3 cm describes a cone with minimum volume. Determine cone dimensions.
• Square pyramid Calculate the pyramid's volume with the side 5cm long and with a square base, side-base has an angle of 60 degrees.
• 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'.
• Cone Calculate volume and surface area of ​​the cone with a diameter of the base d=15 cm and side of the cone with the base has angle 52°.
• Rotary cone The volume of the rotation of the cone is 472 cm3 and angle between the side of the cone and base angle is 70°. Calculate lateral surface area of this cone.
• 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.
• Pentagonal prism The regular pentagonal prism is 10 cm high. The radius of the circle of the described base is 8 cm. Calculate the volume and surface area of the prism.
• 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? What is the volume of a quadrilateral oblique prism with base edges of length a = 1m, b = 1.1m, c = 1.2m, d = 0.7m, if a side edge of length h = 3.9m has a deviation from the base of 20° 35' and the edges a, b form an angle of 50.5°.
• Horizontal Cylindrical Segment How much fuel is in the horizontal cylindrical segment tank with a length of 10m, the width of level 1 meter, and the level is 0.2 meters below the tank's upper side?
• Cylinder horizontally The cylinder with a diameter of 3 m and a height/length of 15 m is laid horizontally. Water is poured into it, reaching a height of 60 cm below the axis of the cylinder. How many hectoliters of water is in the cylinder?

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