# Surface area + expression of a variable from the formula - math problems

- 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. - Pentagonal prism

The regular pentagonal prism is 10 cm high. The radius of the circle of the described base is 8 cm. Calculate the volume and surface area of the prism. - Two hemispheres

In a wooden hemisphere with a radius r = 1, a hemispherical depression with a radius r/2 was created so that the bases of both hemispheres lie in the same plane. What is the surface of the created body (including the surface of the depression)? - 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? - Diameter = height

The surface of the cylinder, the height of which is equal to the diameter of the base, is 4239 cm square. Calculate the cylinder volume. - The Earth

The Earth's surface is 510,000,000 km^{2}. Calculates the radius, equator length, and volume of the Earth, assuming the Earth has the shape of a sphere. - The regular

The regular quadrilateral pyramid has a volume of 24 dm^{3}and a height of 45 cm. Calculate its surface. - 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. - 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. - Block or cuboid

The wall diagonals of the block have sizes of √29cm, √34cm, √13cm. Calculate the surface and volume of the block. - Two rectangular boxes

Two rectangular boxes with dimensions of 5 cm, 8 cm, 10 cm, and 5 cm, 12 cm, 1 dm are to be replaced by a single cube box of the same cubic volume. Calculate its surface. - Tropics and polar zones

What percentage of the Earth’s surface lies in the tropical, temperate and polar zone? Individual zones are bordered by tropics 23°27' and polar circles 66°33' - Quadrilateral prism

Calculate the volume (V) and the surface (S) of a regular quadrilateral prism whose height is 28.6 cm and the deviation of the body diagonal from the base plane is 50°. - 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 cm^{3}(l). - Top of the tower

The top of the tower has the shape of a regular hexagonal pyramid. The base edge has a length of 1.2 m, the pyramid height is 1.6 m. How many square meters of sheet metal is needed to cover the top of the tower if 15% extra sheet metal is needed for joint - Sum of the edges

The sum of the lengths of all edges of the cube is 72 cm. How many cm^{2}of colored paper are we going to use for sticking? - Hexagonal pyramid

Calculate the surface area of a regular hexagonal pyramid with a base inscribed in a circle with a radius of 8 cm and a height of 20 cm. - Quadrilateral pyramid

In a regular quadrilateral pyramid, the side edge is e = 7 dm and the diagonal of the base is 50 cm. Calculate the pyramid shell area. - Rectangular base pyramid

Calculate an area of the shell of the pyramid with a rectangular base of 2.8 m and 1.4 m and height 2.5 meters. - The ball

The ball has a radius of 2m. What percentage of the surface and volume is another sphere whose radius is 20% larger?

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