Area of shape + surface area - math problems
Number of problems found: 114
- Sphere in cone
A sphere is inscribed in the cone (the intersection of their boundaries consists of a circle and one point). The ratio of the surface of the ball and the contents of the base is 4: 3. A plane passing through the axis of a cone cuts the cone in an isoscele - Edge of prism
The regular quadrilateral prism has a surface of 250 dm2, its shell has a content of 200 dm2. Calculate its leading edge. - Largest wall
Find the content of the largest wall of a prism with the base of a rectangle which has a height of 4 dm, side c = 5 cm, and side b = 6 cm. - Quadrilateral prism
Calculate the surface of a quadrilateral prism according to the input: Area of the diamond base S1 = 2.8 m2, length of the base edge a = 14 dm, height of the prism 1,500 mm. - Quadrilateral prism
The surface of the regular quadrilateral prism is 8800 cm2, the base edge is 20 cm long. Calculate the volume of the prism - The tent
Calculate how much cover (without a floor) is used to make a tent that has the shape of a regular square pyramid. The edge of the base is 3 m long and the height of the tent is 2 m. - Quadrilateral pyramid
Calculate the surface of a quadrilateral pyramid, which has a rectangular base with dimensions a = 8 cm, b = 6 cm and height H = 10 cm. - Triangular prism
Calculate the surface of a regular triangular prism, the edges of the base are 6 cm long and the height of the prism is 15 cm. - Cutting the prism
A prism with a square base with a content of 1 cm2 and a height of 3 cm was cut from a cube with an edge length of 3 cm. What is the surface of the body formed from the cube after cutting the prism? - The hollow cylinder
The hollow cylinder has a height of 70 cm, an outer diameter of 180 cm and an inner diameter of 120 cm. What is the surface of the body, including the area inside the cavity? - Wallpaper
3750 cm square of wallpaper is needed to glue a cube-shaped box. Can Dad cut out the whole necessary piece of wallpaper as a whole if he has a roll of wallpaper 50 cm wide? - Fire tank
1428 hl of water is filled in a block-shaped fire tank with the edges of the base 12 m and 7 m. Calculate the content of water-wetted areas. - Triangular prism
The base of the perpendicular triangular prism is a rectangular triangle with a hypotenuse of 10 cm and one leg of 8 cm. The prism height is 75% of the perimeter of the base. Calculate the volume and surface of the prism. - Triangular prism,
The regular triangular prism, whose edges are identical, has a surface of 2514 cm ^ 2 (square). Find the volume of this body in cm3 (l). - Triangular prism
Calculate the surface of a triangular prism with the base of an equilateral triangle with a side length of 7.5 cm and a corresponding height of 6.5 cm. Prism height is 15cm. - Two bodies
The rectangle with dimensions 8 cm and 4 cm is rotated 360º first around the longer side to form the first body. Then, we similarly rotate the rectangle around the shorter side b to form a second body. Determine the ratio of surfaces of the first and seco - Tetrahedral pyramid
Determine the surface of a regular tetrahedral pyramid when its volume is V = 120 and the angle of the sidewall with the base plane is α = 42° 30´. - Surface of the cylinder
Calculate the surface of the cylinder for which the shell area is Spl = 20 cm2 and the height v = 3.5 cm - The plaster cast
The plaster cast has the shape of a regular quadrilateral pyramid. The cover consists of four equilateral triangles with a 5 m side. Calculate its volume and surface area. - Base of prism
The base of the perpendicular prism is a rectangular triangle whose legs length are at a 3: 4 ratio. The height of the prism is 2cm smaller than the larger base leg. Determine the volume of the prism if its surface is 468 cm2.
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