A rectangular container, whose base is a square of side 5 cm, stands on a horizontal table, and holds water upto 1 cm from the top. When a cube is placed in the water it is completely submerged, the water rises to the top and 2 cubic cm of water overflows. Calculate the volume of the cube and also the length of its edge.
Answers
Volume of the cube = 27 cubic cm
Length of the edge = 3 cm
Step-by-step explanation:
Step 1 :
The square side of the rectangular container = 5 cm
The height of the container without water = 1 cm
Hence the volume of the container not filled with water = Area of the base × height of the container not filled with water = 5 × 5 × 1 = 25 cubic cm
Step 2 :
Given that when the cube is fully immersed inside the container 2 cubic cm of water over flows
Volume of the water which has overflowed = 2 cubic cm
The volume of the cube = Volume of the container not filled with water + the volume of the water which has overflowed
Hence volume of the cube = 25 + 2 = 27 cubic cm
Step 3 :
Let l be the length of the edge of the cube.
Then volume of the cube = l³ = 27
Therefore length of the edge l = ∛27 = 3 cm
Step 4 :
Answer :
Volume of the cube = 27 cubic cm
Length of the edge = 3 cm
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Answer:
Volume of the cube = 27 cubic cm
Length of the edge = 3 cm
Step-by-step explanation:
Step 1 :
The square side of the rectangular container = 5 cm
The height of the container without water = 1 cm
Hence the volume of the container not filled with water = Area of the base × height of the container not filled with water = 5 × 5 × 1 = 25 cubic cm
Step 2 :
Given that when the cube is fully immersed inside the container 2 cubic cm of water over flows
Volume of the water which has overflowed = 2 cubic cm
The volume of the cube = Volume of the container not filled with water + the volume of the water which has overflowed
Hence volume of the cube = 25 + 2 = 27 cubic cm
Step 3 :
Let l be the length of the edge of the cube.
Then volume of the cube = l³ = 27
Therefore length of the edge l = ∛27 = 3 cm
Step 4 :
Answer :
Volume of the cube = 27 cubic cm
Length of the edge = 3 cm
