# Surface area - high school - math problems

- Hexagon

Calculate the surface of a regular hexagonal prism whose base edge a = 12cm and side edge b = 3 dm. - Sphere radius

The radius of the sphere we reduce by 1/3 of the original radius. How much percent does the volume and surface of the sphere change? - Seat

How much m² of fabric do we need to sew a 50cm-shaped cube-shaped seat if 10% of the material we add to the folds? - Surface of the cylinder

Calculate the surface of the cylinder for which the shell area is Spl = 20 cm^{2}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. - Prism diagonal

The body diagonal of a regular square prism has an angle of 60 degrees with the base, the edge length is 10 cm. What is the volume of the prism? - Spherical cap 4

What is the surface area of a spherical cap, the base diameter 20 m, height 2.5 m? Calculate using formula. - Axial cut of a rectangle

Calculate the volume and surface of the cylinder whose axial cut is a rectangle 15 cm wide with a diagonal of 25 cm long. - Tetrahedral pyramid

A regular tetrahedral pyramid is given. Base edge length a = 6.5 cm, side edge s = 7.5 cm. Calculate the volume and the area of its face (side 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 cm^{2}. - Space diagonal

The space diagonal of a cube is 129.91 mm. Find the lateral area, surface area and the volume of the cube. - Two cubes

The surfaces of two cubes, one of which has an edge of 22 cm longer than the second are differ by 19272 cm^{2}. Calculate the edge length of both cubes. - 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. - Right triangular prism

We have cuboid with a base and dimensions of 12 cm and 5 cm and height of 4 cm. The tablecloth cut it into two identical triangular prisms with right triangular bases. The surface of the created prisms was painted with color. Calculate the surface area of. - Cylindrical container

An open-topped cylindrical container has a volume of V = 3140 cm^{3}. Find the cylinder dimensions (radius of base r, height v) so that the least material is needed to form the container. - Conical area

A right angled triangle has sides a=12 and b=19 in right angle. The hypotenuse is c. If the triangle rotates on the c side as axis, find the volume and surface area of conical area created by this rotation. - Calculate 3

Calculate the cube volume whose edge is 3x-1,3x-1,3x-1 - Tropical, mild and arctic

How many percents of the Earth's surface lies in the tropical, mild and arctic range? The border between the ranges is the parallel 23°27 'and 66°33'. - Cuboid walls

Calculate the volume of the cuboid if its different walls have area of 195cm², 135cm² and 117cm². - Nice prism

Calculate the surface of the cuboid if the sum of its edges is a + b + c = 19 cm and the body diagonal size u = 13 cm.

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