Jenny made a block with small cubes
of 9 cubic cm volume. To make the
block she used 4 small cubes long, 8
small cubes wide and 16 small cubes
deep. She realizes that she has used
more small cubes than she really
needed. She realized that she could
have glued a fewer number of cubes
together to look like a block with same
dimensions, if it were made hollow.
What is the minimum number of cubes
that she needs to take out so that the
bigger cube is hollow?
342
168
512
344
Answers
Answer:
Step-by-step explanation:
Volume of small cubes = 9 cubic cm (Given)
Dimensions of the cube = 4 x 8 x 16 (Given)
Cutting the cube into three layers – top, middle and bottom.
To get a hollow cube, we need the top and the bottom layer and from the middle layer, if we remove the core that is the unpainted cubes, we will get the material for the hollow cube.
Initially we have 4 x 8 x 16 cubes = 512 small cubes, thus forming a solid cube.
The top layer has 1 x 8 x 16 cubes = 128 cubes that are needed for the hollow cube and similarly we need 128 cubes from the bottom also.
In the middle layer, we have again 128 cubes. Thus,
Core = (4-2) × (8-2) × (16-2)
= 2 × 6 × 14
= 168
Thus, the total no. of cubes needed to make a hollow cube is
= 512- 128
= 344
Answer:
Step-by-step explanation:
Volume of small cubes = 9 cubic cm (Given)
Dimensions of the cube = 4 x 8 x 16 (Given)
Cutting the cube into three layers – top, middle and bottom.
To get a hollow cube, we need the top and the bottom layer and from the middle layer, if we remove the core that is the unpainted cubes, we will get the material for the hollow cube.
Initially we have 4 x 8 x 16 cubes = 512 small cubes, thus forming a solid cube.
The top layer has 1 x 8 x 16 cubes = 128 cubes that are needed for the hollow cube and similarly we need 128 cubes from the bottom also.
In the middle layer, we have again 128 cubes. Thus,
Core = (4-2) × (8-2) × (16-2)
= 2 × 6 × 14
= 168
Thus, the total no. of cubes needed to make a hollow cube is
= 512- 128
= 344