Three cubes

The body was created by gluing three identical cubes. Its volume is 192 cm³. What is its surface in dm²?

Correct answer:

S =  2.24 dm²

Step-by-step explanation:

$$\begin{gathered} V=192{\text{cm}}_3 \\ {V}_1=V\mathrm{/}3=192\mathrm{/}3=64{\text{cm}}^3 \\ a=\sqrt[3]{V_1}=\sqrt[3]{64}=4\text{ cm } \\ {a}_2=a\mathrm{/}10=4\mathrm{/}10={\displaystyle \frac{2}{5}}=0.4\text{ dm } \\ {S}_1=a_2^2=0.4^2={\displaystyle \frac{4}{25}}=0.16{\text{dm}}^2 \\ S=3\cdot 6\cdot S_1-4\cdot S_1=3\cdot 6\cdot 0.16-4\cdot 0.16={\displaystyle \frac{56}{25}}={\displaystyle \frac{56}{25}}{\text{dm}}^2=2.24{\text{dm}}^2 \end{gathered}$$

Try another example

Related math problems and questions:

• Three cubes
  Two cube-shaped boxes with edges a = 70 cm; b = 90 cm must be replaced by one cube-shaped box. What will be its edge?
• Regular square prism
  The volume of a regular square prism is 192 cm³. The size of its base edge and body height are 1: 3. Calculate the surface of the prism.
• 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.
• Four prisms
  Question No. 1: The prism has the dimensions a = 2.5 cm, b = 100 mm, c = 12 cm. What is its volume? a) 3000 cm² b) 300 cm² c) 3000 cm³ d) 300 cm³ Question No.2: The prism base is a rhombus with a side length of 30 cm and a height of 27 cm. The height of t
• Volume from surface area
  What is the volume of the cube whose surface area is 96 cm²?
• Cube 6
  Volume of the cube is 216 cm³, calculate its surface area.
• Rotary cylinder
  In the rotary cylinder it is given: surface S = 96 cm² and volume V = 192 cm cubic. Calculate its radius and height.
• Two boxes-cubes
  Two boxes cube with edges a=38 cm and b = 81 cm is to be replaced by one cube-shaped box (same overall volume). How long will be its edge?
• 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?
• Equilateral cylinder
  Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 199 cm³ . Calculate the surface area of the cylinder.
• Cubes
  Cube, which consists of 8 small cubes with edge 3 dm has volume:
• Cubes
  Surfaces of cubes, one of which has an edge of 48 cm shorter than the other, differ by 36288 dm². Determine the length of the edges of this cubes.
• Cone - from volume surface area
  The volume of the rotating cone is 1,018.87 dm³, and its height is 120 cm. What is the surface area of the cone?
• Volume and area
  What is the volume of a cube which has an area of 361 cm²?
• Cuboids in cube
  How many cuboids with dimensions of 6 cm, 8 cm and 12 cm can fit into a cube with side 96 centimeters?
• 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 the surface of the prism?
• Cube 9
  What was the cube's original edge length after cutting 39 small cubes with an edge of 2 dm left 200 dm³?