# Cube root - problems

- Perfect cubes

Suppose a number is chosen at random from the set (0,1,2,3,. .. ,202). What is the probability that the number is a perfect cube? - The volume 2

The volume of a cube is 27 cubic meters. Find the height of the cube. - Cube diagonals

Calculate the length of the side and the diagonals of the cube with a volume of 27 cm^{3}. - Cube in a sphere

The cube is inscribed in a sphere with volume 8818 cm^{3}. Determine the length of the edges of a cube. - Z9-I-4

Kate thought a five-digit integer. She wrote the sum of this number and its half at the first line to the workbook. On the second line wrote a total of this number and its one fifth. On the third row she wrote a sum of this number and its one nines. Fi - Transforming cuboid

Cuboid with dimensions 8 cm, 13 and 16 cm is converted into a cube with the same volume. What is its edge length? - Eiffel Tower

Eiffel Tower in Paris is 300 meters high, is made of steel. Its weight is 8000 tons. How tall is the tower model made of the same material, if it weigh is 2.4 kg? - Prism X

The prism with the edges of the lengths x cm, 2x cm and 3x cm has volume 20250 cm^{3}. What is the area of surface of the prism? - Cone

Circular cone with height h = 29 dm and base radius r = 3 dm slice plane parallel to the base. Calculate distance of the cone vertex from this plane, if solids have the same volume. - Rotary cone

The volume of the rotation of the cone is 472 cm^{3}and angle between the side of the cone and base angle is 70°. Calculate lateral surface area of this cone. - Balls

Three metal balls with volumes V_{1}=71 cm^{3}V_{2}=78 cm^{3}and V_{3}=64 cm^{3}melted into one ball. Determine it's surface area. - Cylinder

Calculate the dimensions of rotating cylindrical container with volume 2 l, if height of container is equal to the diameter of the base. - Rotary cone

Rotary cone whose height is equal to the circumference of the base, has a volume 229 cm^{3}. Calculate the radius of the base circle and height of the cone. - Lead cube

Calculate the edge of the cube made from lead, which weighs 19 kg. The density of lead is 11341 kg/m^{3}. - Hollow sphere

Steel hollow sphere floats on the water plunged into half its volume. Determine the outer radius of the sphere and wall thickness, if you know that the weight of the sphere is 0.5 kg and density of steel is 7850 kg/m^{3} - 3y inflation

Price of the roll rise in the first year by 9%, the second year fell by 5% and in the third year increased by 3%. Calculate the average annual increase in price of the roll. - Plasticine ball

Plasticine balls have radius r_{1}=85 cm, r_{2}=60 mm, r_{3}=59 cm, r_{4}=86 cm, r_{5}=20 cm, r_{6}=76 mm, r_{7}=81 mm, r_{8}=25 mm, r_{9}=19 mm, r_{10}=14 cm. For these balls. - Root

Use law of square roots roots: ? - Shots

5500 lead shots with diameter 4 mm is decanted into a ball. What is it diameter? - Iron sphere

Iron sphere has weight 100 kg and density ρ = 7600 kg/m^{3}. Calculate the volume, surface and diameter of the sphere.

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