Surface of cubes

Peter molded a cuboid 2 cm, 4cm, 9cm of plasticine. Then the plasticine split into two parts in a ratio 1:8. From each piece made a cube. In what ratio are the surfaces of these cubes?

Correct result:

p =  1:4

Solution:

$$\begin{gathered} V=2\cdot 4\cdot 9=72{\text{cm}}^3 \\ {V}_1={\displaystyle \frac{1}{1+8}}\cdot V={\displaystyle \frac{1}{1+8}}\cdot 72=8{\text{cm}}^3 \\ {V}_2={\displaystyle \frac{8}{1+8}}\cdot V={\displaystyle \frac{8}{1+8}}\cdot 72=64{\text{cm}}^3 \\ {a}_1=\sqrt[3]{V_1}=\sqrt[3]{8}=2\text{ cm } \\ {a}_2=\sqrt[3]{V_2}=\sqrt[3]{64}=4\text{ cm } \\ {S}_1=6\cdot a_1^2=6\cdot 2^2=24\text{ cm } \\ {S}_2=6\cdot a_2^2=6\cdot 4^2=96\text{ cm } \\ p=S_1\mathrm{/}{S}_2=24\mathrm{/}96={\displaystyle \frac{1}{4}}=0.25=1:4 \end{gathered}$$

Try another example

Showing 0 comments:

Next similar math problems:

• 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?
• 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.
• Two bodies
  The rectangle with dimensions 8 cm and 4 cm is rotated 360º first around the longer side to form the first body. Then, we similarly rotate the rectangle around the shorter side b to form a second body. Determine the ratio of surfaces of the first and seco
• Mystery of stereometrie
  Two regular tetrahedrons have surfaces 88 cm² and 198 cm². In what ratio is their volumes? Write as a fraction and as a decimal rounded to 4 decimal places.
• Prism bases
  Volume perpendicular quadrilateral prism is 360 cm³. The edges of the base and height of the prism are in the ratio 5:4:2 Determine the area of the base and walls of the prism.
• Plasticine ball
  Plasticine balls have radius r₁=85 cm, r₂=60 mm, r₃=59 cm, r₄=86 cm, r₅=20 cm, r₆=76 mm, r₇=81 mm, r₈=25 mm, r₉=19 mm, r₁₀=14 cm. For these balls
• Cuboid and ratio
  Cuboid has dimensions in ratio 1:2:6 and the surface area of the cuboid is 1000 dm². Calculate the volume of the cuboid.
• Two cubes
  The surfaces of two cubes, one of which has an edge of 22 cm longer than the second are differ by 19272 cm². Calculate the edge length of both cubes.
• Cuboid edges in ratio
  Cuboid edges lengths are in ratio 2:4:6. Calculate their lengths if you know that the cuboid volume is 24576 cm³.
• Ratio of edges
  The dimensions of the cuboid are in a ratio 3: 1: 2. The body diagonal has a length of 28 cm. Find the volume of a cuboid.
• Cuboid - ratios
  The sizes of the edges of the cuboid are in the ratio 2: 3: 5. The smallest wall have area 54 cm². Calculate the surface area and volume of this cuboid.
• Cuboid - edges
  The cuboid has dimensions in ratio 4: 3: 5, the shortest edge is 12 cm long. Find: (A) the lengths of the remaining edges, (B) the surface of the cuboid, (C) the volume of the cuboid
• Sphere parts, segment
  A sphere with a diameter of 20.6 cm, the cut is a circle with a diameter of 16.2 cm. .What are the volume of the segment and the surface of the segment?
• Sugar cubes
  The glass has 600 ml of tea, which represents 80% of the volume of the glass. If you put twenty regular sugar cubes of 2 cm in the tea, how many ml of tea are poured?
• 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.
• Prism
  Calculate the height of the prism having a surface area 448.88 dm² wherein the base is square with a side of 6.2 dm. What will be its volume in hectoliters?
• Cuboid surface
  Determine surface area of cuboid if its volume is 52.8 cm cubic and length of the two edges are 2 cm and 6 cm.