Cube root - examples
- Minimum surface
Find the length, breadth, and height of the cuboid shaped box with a minimum surface area, into which 50 cuboid shaped blocks, each with length, breadth and height equal to 4 cm, 3 cm and 2 cm respectively can be packed.
- Pyramid cut
We cut the regular square pyramid with a parallel plane to the two parts (see figure). The volume of the smaller pyramid is 20% of the volume of the original one. The bottom of the base of the smaller pyramid has a content of 10 cm2. Find the area of the o
- Cube root
Find cube root of 18
- Cube in a sphere
The cube is inscribed in a sphere with volume 3724 cm3. Determine the length of the edges of a cube.
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 11 cm, 9 and 11 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 cm3. What is the area of surface of the prism?
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 cm3 and angle between the side of the cone and base angle is 70°. Calculate lateral surface area of this cone.
Three metal balls with volumes V1=71 cm3 V2=78 cm3 and V3=64 cm3 melted into one ball. Determine it's surface area.
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 cm3. 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/m3.
- 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/m3
- 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 r1=75 cm, r2=35 cm, r3=91 cm. For these balls are molded one big ball. Calculate the radius r of the resulting ball.
Use law of square roots roots: ?
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/m3. Calculate the volume, surface and diameter of the sphere.