Triangle + Pythagorean theorem - practice problems - page 21 of 60
Number of problems found: 1188
- Pyramid in cube
In a cube with an edge 12 dm long, we have an inscribed pyramid with the apex at the center of the cube's upper wall. Calculate the volume and surface area of the pyramid. - Triangular pyramid
It is given perpendicular regular triangular pyramid: base side a = 5 cm, height v = 8 cm, volume V = 28.8 cm³. What is its area (surface area)? - Dimensions 4700
The toolbox has internal dimensions, a length of 1.5 meters, a width of 80 cm, and a height of 6 dm. Calculate the longest rod we can hide in this box. - Railways
Railways climb 2.8 ‰. Calculate the height difference between two points on the railway distant 5997 meters. - Isosceles + prism
Calculate the volume of the perpendicular prism if its height is 17.5 cm and the base is an isosceles triangle with a base length of 5.8 cm and an arm's length of 3.7 cm - Rotating cone
Find the rotating cone's surface and volume if its side is 150 mm long and the circumference of the base is 43.96 cm. - Lateral surface area
The ratio of the area of the base of the rotary cone to its lateral surface area is 3:5. Calculate the surface and volume of the cone if its height v = 4 cm. - Cube diagonals
Determine the volume and surface area of the cube if you know the length of the body diagonal u = 216 cm. - Decimetres 4163
Determine the length of the body and wall diagonals of the cube, the volume of which is equal to 0.343 decimetres. Also, calculate its surface. - Lengths of medians from coordinates
There is a triangle ABC: A [-6.6; 1.2], B [3.4; -5.6], C [2.8; 4.2]. Calculate the lengths of its medians. - Calculate 30961
Calculate the cone's surface and volume if its base diameter is 12 cm and the height is 150 mm. - Triangular pyramid
Calculate the volume of a regular triangular pyramid with edge length a = 12cm and pyramid height v = 20cm. - Nice prism
Calculate the cuboid's surface if the sum of its edges is a + b + c = 19 cm and the body diagonal size u = 13 cm. - Cone and the ratio
The rotational cone has a height of 43 cm, and the ratio of the base surface to the lateral surface is 5: 7. Calculate the surface of the base and the lateral surface. - Triangle 67504
Sestroj triangle HOP, if o = 6 cm, h = 8 cm and | PHO | = 90 ° - Identical 35961
Nine identical spheres are stacked in the cube to fill the volume of the cube as much as possible. What part of the volume will the cube fill? - Perpendicular 35183
Calculate the surface and volume of a vertical prism if its height h = 18 cm and if the base is an equilateral triangle with side length a = 7.5 cm. - Rotating 28001
There is a rotating cone: r = 6.8 cm s = 14.4 cm. Find the area of the cone surface S2, the height h, and the volume V. - Hexagonal pyramid
Find the area of a shell of the regular hexagonal pyramid if you know that its base edge is 5 cm long and the height of this pyramid is 10 cm. - Triangular prism - regular
The regular triangular prism is 7 cm high. Its base is an equilateral triangle whose height is 3 cm. Calculate the surface and volume of this prism.
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