# Surface area + volume - math problems

- Quadrilateral prism

The surface of the regular quadrilateral prism is 8800 cm^{2}, the base edge is 20 cm long. Calculate the volume of the prism - The water tank

The water tank has the shape of a sphere with a radius of 2 m. How many liters of water will fit in the tank? How many kilograms of paint do we need to paint the tank, if we paint with 1 kg of paint 10 m^{2}? - Magnified cube

If the lengths of the edges of the cube are extended by 5 cm, its volume will increase by 485 cm^{3}. Determine the surface of both the original and the magnified cube. - 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. - Volume and surface area

Find the volume and surface of a wooden block with dimensions: a = 8 cm, b = 10 cm, c = 16 cm. - 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. - Surface of the cube

Find the surface of the cube that has volume 1/1m3 2/0.001 m^{3}3/8000 mm^{3} - 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). - 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°. - Hemisphere - roof

The shape of the observatory dome is close to the hemisphere. Its outer diameter is 11 m. How many kilograms of paint and how many liters of paint is used for its double coat if you know that 1 kg of paint diluted with 1 deciliter of paint will paint an a - The ball

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

The quadrilateral pyramid has a rectangular base of 24 cm x 3.2dm and a body height of 0.4m. Calculate its volume and surface area. - Axial section of the cone

The axial section of the cone is an isosceles triangle in which the ratio of cone diameter to cone side is 2: 3. Calculate its volume if you know its area is 314 cm square. - Cone side

Calculate the volume and area of the cone whose height is 10 cm and the axial section of the cone has an angle of 30 degrees between height and the cone side.

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