Volume + angle - practice problems
Number of problems found: 81
- Calculate 82567
The volume of a cuboid with a square base is 64 cm3, and the body diagonal deviation from the base's plane is 45 degrees. Calculate its surface area. - Quadrilateral 82146
Calculate the volume and surface area of a regular quadrilateral prism with base edge a=24 cm if the body diagonal makes an angle of 66° with the base. - 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. - Calculate 80793
The liquid has a specific gravity of γ = 9050 N. m-3. Calculate its specific gravity, the mass of 2 m³ of this liquid, and also of 3 m³ of this liquid. - 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. - Deviation 70434
Frustum has the base radii of the figures r1 and r2: r1> r2, r2 = s, and if the side deviation from the base plane is 60°. Express the surface and volume of the cone frustum using its side s. - 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'. - 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 '. - 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 °. - Right-angled trapezoid
A right-angled trapezoid with the measure of the acute angle of 50° is given. The lengths of its bases are 4 and 6 units. The volume of the solid obtained by rotation of the given trapezoid about the longer base is: - Side wall planes
Find the volume and surface of a cuboid whose side c is 30 cm long and the body diagonal forms angles of 24°20' and 45°30' with the planes of the side walls. - The truncated
The truncated rotating cone has bases with radii r1 = 8 cm, r2 = 4 cm and height v = 5 cm. What is the volume of the cone from which the truncated cone originated? - 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. - Truncated pyramid
Find the volume of a regular 4-sided truncated pyramid if a1 = 14 cm, a2 = 8 cm, and the angle that the side wall with the base is 42 degrees. - 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. - Temperature 37001
The mother prepared half a liter of cold water for the children to drink. It mixed water at 20 ° C with 400 ml of cold water at 5 ° C. What was the temperature of the prepared drink? - Temperature 36991
Honza filled 2 liters of hot water at a temperature of 90 ° C from a heater into a five-liter container. What temperature must the water that the container fills have a mixture temperature of 42 ° C? - Calculate 36253
Calculate the volume of the pyramid, whose base edge a = 8 cm and the sidewall makes an angle α = 60 ° with the square base. - Circumscribed 35781
The regular hexagonal prism is 2 cm high. The radius of the circle circumscribed by the base is 8 cm. Determine its volume and surface.
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