Pythagorean theorem - math word problems - page 56 of 74
Number of problems found: 1468
- Pentagonal pyramid
The height of a regular pentagonal pyramid is as long as the edge of the base, 20 cm. Calculate the volume and surface area of the pyramid. - Space diagonal angles
Calculate the angle between the body diagonal and the side edge c of the block with dimensions: a = 28 cm, b = 45 cm, and c = 73 cm. Then, find the angle between the body diagonal and the plane of the base ABCD. - Triangular prism
The triangular prism has a base in the shape of a right triangle, the legs of which are 9 cm and 40 cm long. The height of the prism is 20 cm. What is its volume cm³? And the surface cm²? - The tent
The tent has the shape of a regular square pyramid. The edge of the base is 3 m long, and the tent's height is 2 m. Calculate how much cover (without a floor) is used to make a tent. - Storm and roof
The roof of the building is a cone with a height of 3 meters and a radius equal to half the height of the roof. How many m² of the roof need to be repaired if 20% were damaged in a storm? - Pyramid Roof Sheet Metal
The roof of the recreation cottage has the shape of a regular four-sided pyramid with a height of 8 m and a base edge of 4 m. How much ℅ went to folds and joints, and 75.9 square meters of sheet metal were used to cover the roof? - Triangular prism
The curved part of the rotating cylinder is four times larger than the area of its base. Determine the volume of the regular triangular prism inscribed in the cylinder. The radius of the bottom of the cylinder is 10 cm. - Ratio of edges
The cuboid dimensions are in a ratio of 3:1:2. The body diagonal has a length of 28 cm. Find the volume of a cuboid. - Calculate cylinder
A cylinder has a volume V = 120 cm³ and a height v = 4 cm. Calculate the radius and the lateral surface area S. - Roof 7
The roof is a regular quadrilateral pyramid with a base edge of 12 m, and a height of 4 m. How many percent is folds and waste if in construction was consumed 181.4 m² of the plate was? - Angle of deviation
The surface of the rotating cone is 30 cm² (with a circle base), and its surface area is 20 cm². Calculate the deviation of this cone's side from the base's plane. - Cylinder surface
The area of the rotating cylinder shell is half the area of its surface. Calculate the surface of the cylinder if you know that the diagonal of the axial section is 5 cm. - Pyramid - angle
Calculate the regular quadrilateral pyramid's surface, the base edge of which is measured 6 cm, and the deviation from the plane of the base's sidewall plane is 50 degrees. - Cube in a sphere
A cube is inscribed in a sphere with volume 8101 cm³. Determine the edge length of the cube. - Cuboid
A cuboid with edge a = 6 cm and space diagonal u = 31 cm has a volume of V = 900 cm³. Calculate the lengths of the other two edges. - Deep pool - bottom
A pool is 25 m long and 12 m wide. In one half of the pool, the depth is constant at 1.8 m; in the other half, the bottom slopes gradually up to a depth of 1.2 m. What is the total area of the pool bottom? - 4B - truncated pyramid
Calculate the volume of a regular truncated quadrilateral pyramid if the base edges are 10 cm and 4 cm and the slant height of the lateral face is 5 cm. - The perimeter
The perimeter of the base of a regular quadrilateral pyramid is the same as its height. The pyramid has a volume of 288 dm³. Calculate its surface area round the result to the whole dm². - The radius
A right circular cone's radius and slant heights are 9 cm and 15 cm, respectively. Find, correct to one decimal place, the (i) Height (ii) Volume of the cone - Axial section
The diagonal of the axial section of the rotating cylinder is 6 cm, and its surface is 30 cm². Calculate the radius of the base.
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