# Volume + cosine - math problems

#### Number of problems found: 10

• 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.
• 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.
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°.
• 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?
• 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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