An equal number of cube(s) of the largest size are cut out from the given cuboid. the maximum increase in perimeter of the remaining part of the
cuboid will be
Answers
Answer:
Step-by-step explanation
We have the cuboid of dimensions 10cm×9cm×6cm
We are to find how many cubes with edge 3 cm can be cut from the given cuboid.
Let us cut this cuboid into following two cuboids
9cm×9cm×6cm
And
1cm×9cm×6cm
So, the number of cubes of sides 3 cm, that can be cut from the first cuboid,
⇒
3cm×3cm×3cm
9cm×9cm×6cm
=18
We can not cut a single cube of side 3 cm from the second cuboid of dimensions 1cm×9cm×6cm
Hence, this much volume is unless for us.
So, we can cut maximum 18 cubes of sides 3cm from the cuboid of dimension 10cm×9cm×6cm.
Question:
An equal number of cube(s) of the largest size are cut out from the given cuboid. The ratio of the maximum possible increase in surface area to the initial surface area is?
Step-by-step explanation:
First, take out the H..C.F. of 8cm, 4cm, and 3cm, we get:
8 = 2 ×2 × 2 ×1
4 = 2 × 2 × 1
3 = 3 × 1
Since, the only common is 1, let's take side of cube to be 1cm.
- Surface area of cube = (6 × side²)
Surface area of cube = 6×1
Surface area of cube = 6m²
- Surface area of cuboid = [2(lb+bh+lh)]
Surface area of cuboid = 2(24+32+12)
Surface area of cuboid = 2 × 68
Surface area of cuboid = 136 m²
- Volume of cube = side³
Volume of cube = (1)³
Volume of cube = 1 cm³
- Volume of cuboid = l × b × h
Volume of cuboid = 8 × 4 × 3
Volume of cuboid = 96 cm³
Now, the number of cubes= Volume of cuboid /Volume of cubes
Number of cubes = 96/1
Number of cubes = 96
Then, Surface area of 96 cubes = 96 × 6cm
Surface area of 96 cubes = 576 m²
∴ Required ratio = 136/575
#SPJ2