Volume + angle - practice problems - page 4 of 5
Number of problems found: 81
- Octahedron
All walls of the regular octahedron are identical equilateral triangles. ABCDEF octahedron edges have a length d = 6 cm. Calculate the surface area and volume of this octahedron. - 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. - Decagon prism
A regular decagon of side a = 2 cm is the base of the perpendicular prism. The side walls are squares. Find the prism volume in cm³, round to two decimal places. - Hexa prism
Determine the volume of the hex prism with an edge base of 4 cm. The body height is 28 cm.
- Beer permille
In the 5 kg of the blood of an adult human after three 10° beers consumed in a short time is 6.6 g of alcohol. How much is it per mille? - Pyramid 8
Calculate the volume and the surface area of a regular quadrangular pyramid with a base side of 9 cm and a side wall with the base has an angle of 75°. - Tetrahedral pyramid
Calculate the regular tetrahedral pyramid's volume and surface if the area of the base is 20 cm² and the deviation angle of the side edges from the plane of the base is 60 degrees. - Circular pool
The pool's base is a circle with a radius r = 10 m, excluding a circular segment that determines the chord length of 10 meters. The pool depth is h = 2m. How many hectoliters of water can fit into the pool? - 4side pyramid
Calculate the volume and surface of the regular four-sided pyramid whose base edge is 4 cm long. The angle from the plane of the sidewall and base plane is 60 degrees.
- Hexagonal pyramid
The pyramid's base is a regular hexagon, which can be circumscribed in a circle with a radius of 1 meter. Calculate the volume of a pyramid 2.5 meters high. - Flowerbed
Flowerbed has the shape of a truncated pyramid. The bottom edge of the base a = 10 m, and the upper base b = 9 m. The deviation angle between the edge and the base is alpha = 45°. What volume is needed to make this flowerbed? How many plants can be plante - Juice box 2
The box with juice has the shape of a cuboid. Internal dimensions are 15 cm, 20 cm, and 32 cm. Suppose the box stays at the smallest base juice level and reaches 4 cm below the upper base. How much internal volume of the box fills juice? How many cm below - Triangular prism
The plane passing through the edge AB and the center of segment CC' of regular triangular prism ABCA'B'C' has an angle with base 22 degrees, |AB| = 6 cm. Calculate the volume of the prism. - Pentagonal pyramid
Calculate the volume of a regular 5-side (pentaprism) pyramid ABCDEV; if |AB| = 7.7 cm and a plane ABV, ABC has angle 37 degrees.
- Total displacement
Calculate the total displacement of the 12-cylinder engine with the diameter of the piston bore B = 8.9 cm and stroke S=1.9 cm of the piston. Help: the crankshaft makes one revolution while the piston moves from the top of the cylinder to the bottom and b - Cuboid diagonal
Calculate the volume and surface area of the cuboid ABCDEFGH, which sides a, b, and c has dimensions in the ratio of 7:8:10. If you know that the diagonal wall AC is 56 cm, and the angle between AC and space diagonal AG is 25 degrees. - Rotary cone
The volume of the rotation of the cone is 472 cm³. The angle between the side of the cone and the base angle is 70°. Calculate the lateral surface area of this cone. - Cut and cone
Calculate the volume of the rotation cone whose lateral surface is a circular arc with radius 15 cm and central angle 63 degrees. - Cone
Calculate the volume and surface area of the cone with a diameter of the base d=15 cm and the side of the cone with the base has angle 52°.
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