# Volume + surface area - math problems The surface of the regular quadrilateral prism is 8800 cm2, the base edge is 20 cm long. Calculate the volume of the prism
2. 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 m2?
3. Magnified cube If the lengths of the edges of the cube are extended by 5 cm, its volume will increase by 485 cm3. Determine the surface of both the original and the magnified cube.
4. 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.
5. Volume and surface area Find the volume and surface of a wooden block with dimensions: a = 8 cm, b = 10 cm, c = 16 cm.
6. 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.
7. The Earth The Earth's surface is 510,000,000 km2. Calculates the radius, equator length, and volume of the Earth, assuming the Earth has the shape of a sphere.
8. The regular The regular quadrilateral pyramid has a volume of 24 dm3 and a height of 45 cm. Calculate its surface.
9. 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.
10. 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.
11. Block or cuboid The wall diagonals of the block have sizes of √29cm, √34cm, √13cm. Calculate the surface and volume of the block.
12. 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.
13. Surface of the cube Find the surface of the cube that has volume 1/1m3 2/0.001 m3 3/8000 mm3
14. 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). 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°.
16. 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
17. 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 has a rectangular base of 24 cm x 3.2dm and a body height of 0.4m. Calculate its volume and surface area.
19. 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.
20. 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.

Do you have an interesting mathematical word problem that you can't solve it? Submit math problem, and we can try to solve it.

We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...