Volume + sine - practice problems
Number of problems found: 16
- Sphere in cone
A sphere of radius 3 cm describes a cone with minimum volume. Determine cone dimensions. - ----------------- 4850
v = 35 m α = 55 ° β = 15 ° ----------------- X =? Calculate: V- barrack volume =? S- barrack area =? - Determine 82032
Determine the volume and surface area of a cone whose slope of length 8 cm makes an angle of 75 degrees with the plane of the base. - 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? - 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. - Square pyramid
Calculate the pyramid's volume with the side 5 cm long and with a square base, and the side base has an angle of 60 degrees. - Calculate 3019
The height is 5 cm, and the size of the angle that the side of the cone with the base makes is 63 degrees. Calculate the surface and volume of this cone. - Spherical section cut
Find the volume of a spherical section if the radius of its base is 10 cm and the magnitude of the central angle ω = 120 degrees. - 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. - Deviation 70744
Calculate the volume and surface of the rotating cone if its height is 10 cm and the side has a deviation of 30 ° from the base plane. - 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'. - Hypotenuse 64694
Point S is the center of the hypotenuse AB of the right triangle ABC. Calculate the content of triangle ABC if the line on the hypotenuse is 0.2 dm long and if | ∢ACS | = 30 °. - Magnitudes 64704
The triangle ABC determines the size of the sides a and b and the magnitudes of the interior angles β and γ, given c = 1.86 m, the line on the side c is 2.12 m, and the angle alpha is 40 ° 12 '. - Quadrilateral oblique 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°? - Horizontal 64864
The meter stick is located on the meridian plane and deviated from the horizontal plane to the north by an angle of magnitude 70°. Calculate the length of the shadow cast by a meter stick at true noon if the Sun culminates at an angle of 41°03'. - Water channel
The cross-section of the water channel is a trapezoid. The bottom width is 19.7 m, the water surface width is 28.5 m, and the side walls have a slope of 67°30' and 61°15'. Calculate how much water flows through the channel in 5 minutes if the water flows
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