The cube

The cube has an edge of 12 dm. The second cube has an edge exactly 20% longer. How many % is more water in the second cube than in the first cube, if the first cube is full to 3/4 and the second to 3/8?

Correct answer:

p =  -13.6 %

Step-by-step explanation:

$$\begin{gathered} a_1=12\text{ dm } \\ {a}_2=(1+{\displaystyle \frac{20}{100}})\cdot a_1=(1+{\displaystyle \frac{20}{100}})\cdot 12={\displaystyle \frac{72}{5}}=14.4\text{ dm } \\ {V}_1={\displaystyle \frac{3}{4}}\cdot a_1^3={\displaystyle \frac{3}{4}}\cdot 12^3=1296{\text{dm}}^3 \\ {V}_2={\displaystyle \frac{3}{8}}\cdot a_2^3={\displaystyle \frac{3}{8}}\cdot 14.4^3=1119.744{\text{dm}}^3 \\ p=100\cdot {\displaystyle \frac{V_2-V_1}{V_1}}=100\cdot {\displaystyle \frac{1119.744-1296}{1296}}=-{\displaystyle \frac{68}{5}}\mathrm{\%}=-13.6\mathrm{\%} \end{gathered}$$

Try another example

Related math problems and questions:

• Sea water
  Seawater contains about 4.3% salt. How many dm³ of distilled water we must pour into 5 dm³ of sea water to get water with 1.8% salt?
• Cube zoom
  How many percents do we increase the volume and surface of the cube if we magnify its edge by 38 %?
• Water tank 2
  Water tank cuboid is 12 meters long and 6.5 meters wide and 1.2 meters high. How many hectoliters are in the tank when it is filled to 81%?
• Reduce of the volume
  Calculate how many % reduce the volume of the cube is we reduced length of each edge by 10%.
• Surface area 2
  Calculate how many % reduce the surface area of the cube is we reduced length of each edge by 10%.
• Water level
  The glass container has a cuboid shape with dimensions of the bottom 24 cm and 12 cm. The height of the water is 26 cm. Calculate the body's volume, which is sunk into the water if the water level rise by 3 cm.
• Cinema tickets
  Cinema sold 180 tickets this Thursday, which is 20%. Monday 14%, Tuesday 6%, Wednesday 9%, Friday 24%, Saturday 12%, and Sunday 15%. How many tickets were sold per week?
• Cube and water
  How many liters of water can fit into a cube with an edge length of 0.11 m?
• Cube wall
  The surface of the first cube wall is 64 m². The second cube area is 40% of the surface of the first cube. Determine the length of the edge of the second cube (x).
• Ice and water
  We want to cover rectangular rink with dimensions of 55 m and 25 m with 4cm thick layer of ice. How many liters of water we need if after freezing water increases its volume by 10%?
• Metal sheet
  How much m ^ 2 of sheet metal is needed to beat a box in the shape of a cube with an edge length of 50 cm, if we add 20% on the folds of the lid and walls?
• Hole
  In the center of the cube with edge 14 cm we will drill cylinder shape hole. Volume of the hole must be 27% of the cube. What drill diameter should be chosen?
• Barrel 2
  Empty barrel weighs 7 kg. When it filled with water up to 45% height, weighs 60 kg. How heavy is barrel full of water?
• Energy saving
  They were released three different, independent inventions saving 20%, 24% and 15% energy. Some considered that while the use of these inventions, the total savings will be 20% + 24% + 15% = 59%. Is this true? How much percent of energy will save all thre
• Cube 9
  What was the cube's original edge length after cutting 39 small cubes with an edge of 2 dm left 200 dm³?
• Cylinder in cube
  Into a paper box in the shape of a cube with an edge of 10 cm is placed a can in the shape of a cylinder with a height of 10 cm and touching all the walls of the cube. What % of the volume of the cube does the can take up?
• Cubes
  Cube, which consists of 8 small cubes with edge 3 dm has volume: