Geometry - math word problems - page 162 of 165
Number of problems found: 3289
- Determine the surface area
Find the surface area of a cone of height 30 cm whose slant side makes an angle of 60° with the base plane. - 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. - Rotary cone
The volume of the rotation of the cone is 733 cm³. The angle between the side of the cone and the base angle is 75°. Calculate the lateral surface area of this cone. - Angle of two lines
There is a regular quadrilateral pyramid ABCDV; | AB | = 4 cm; height v = 6 cm. Determine the angles of lines AD and BV. - Calculate a cone
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. - Diagonal
Determine the dimensions of a cuboid whose space diagonal is 60 dm and makes an angle of 35° with one edge and 77° with another edge. - Glass of juice
A cylindrical glass 13 cm tall with a base diameter of 9 cm is filled with juice to a level 3 cm below the rim. Determine the maximum angle to which the glass can be tilted without the juice spilling. - Book Store
The Mabini Book Store (MBS) is reducing the prices of Mathematics books for promotion. The store has 6 Algebra books, 6 Geometry books, and 5 Statistics books to be arranged on a shelf. Books of the same kind are to be placed beside each other. How many w - 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. - Perpendicular direction
A speedboat moves relative to the water at a constant speed of 13 m/s. The speed of the water current in the river is 5 m/s a) At what angle concerning the water current must the boat sail to keep moving perpendicular to the banks of the river? b) At what - Quadrilateral pyramid
The regular quadrilateral pyramid has a base edge a = 1.56 dm and a height h = 2.05 dm. Calculate: a) the deviation angle of the sidewall plane from the base plane b) deviation angle of the side edge from the plane of the base - Octagonal pyramid
Find the volume of a regular octagonal pyramid with height v = 100 and the angle of the side edge with the base plane is α = 60°. - Aircraft climbing
The average climb angle of the aircraft is 11° 20', and its average speed is 400 km/h. How long does it take to climb to a height of 3000 m? - Prism diagonal
The body diagonal of a regular square prism has an angle of 60 degrees with the base, and the edge length is 10 cm. What is the volume of the prism? - Side deviation
A frustum has base radii r₁ and r₂ where r₁ > r₂, r₂ = s, and the slant side makes an angle of 60° with the base plane. Express the surface area and volume of the frustum in terms of its slant height s. - Vertex angle - cone
The rotating cone has a height of 72 cm and an angle at the top of 72°. Determine the volume of a sphere with the same radius as the cone. - Pyramid 8 Calculate the volume and the surface area of a regular quadrilateral pyramid with a base side of 9 cm and a side wall with the base has an angle of 75°.
- Calculate cuboid
Given cuboid ABCDEFGH. We know that |AB| = 1 cm, |BC| = 2 cm, |AE| = 3 cm. Calculate in degrees the angle size formed by the lines BG and FH . - The roof
The tower's roof has the shape of a regular quadrilateral pyramid, the base edge of which is 11 m long, and the side wall of the animal with the base at an angle of 57°. Calculate how much roofing we need to cover the entire roof if we count on 15% waste. - Sphere submerged in the cone
A right circular cone with a top width of 24 cm and an altitude of 8 cm is filled with water. A spherical steel ball with a radius of 3.0 cm is submerged in the cone. Find the volume of water below the sphere.
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