Question

A cube is cut with 3 straight cuts . Either horizontally or vertically . What is the percent increased in the total surface area of the cube​

Answer 1

Answer:

The percent increased in the total surface area of the cube is 66.67 %.

Step-by-step explanation:

Given that:

A cube is cut with 3 straight cuts, either horizontally or vertically.

To Find:

What is the percent increased in the total surface area of the cube.

Let us assume:

The edge of the cube be 3a.

We know that:

⍟ Total surface area of a cube = 6 × (Edge)² ⍟

Total surface area = 6 × (3a)²

Total surface area = 6 × 9a²

Total surface area = 54a²

But when a cube is cut with 3 straight cuts, then three cuboid will be formed having:

Dimension of each cuboid.

Length = 3a

Breadth = 3a/3 = a

Height = 3a

We know that:

⍟ T.S.A. of a cuboid = 2[(LB) + (BH) + (HL)] ⍟

Where,

T.S.A. = Total surface area

L = Length

B = Breadth

H = Height

T.S.A. of three cuboid = 3 × 2[(3a × a) + (a × 3a) + (3a × 3a)]

T.S.A. of three cuboid = 6[3a² + 3a² + 9a²]

T.S.A. of three cuboid = 6[15a²]

T.S.A. of three cuboid = 90a²

Finding the percent increased in the total surface area of the cube:

We have:

Initial area = 54a²

Final area = 90a²

Increased in area = 90a² - 54a²

Increased in area = 36a²

⍟ Increased percent = (Increased in area × 100)/Initial area % ⍟

Increased percent = (36a² × 100)/54a² %

Increased percent = 3600a²/54a² %

Increased percent = 66.67 % (approx.)

Hence,

The percent increased in the total surface area of the cube is 66.67 %.

Answer 2

Given :- A cube is cut with 3 straight cuts . Either horizontally or vertically . What is the percent increased in the total surface area of the cube ?

Answer :-

Let us assume that, the cube has a side of 3x unit .

so,

→ TSA of initial cube before cut = 6(side)² = 6(3x)² = 54x² .

now, when cubes is cut with 3 straight cuts, lets say it cuts with horizontally, then, one side will cut into 3 parts of x cm each and rest will be same . similarly, if cuts vertically .

conclusion :-

• we gets three cuboid of side as x unit, 3x unit and 3x unit .

then,

→ TSA of resulting 3 cuboid so formed = 3*2[lb + bh + hl] = 6[x*3x + 3x*3x + 3x*x] = 6 * 15x² = 90x²

therefore,

→ Increased TSA = 90x² - 54x² = 36x² .

hence,

→ % increased in TSA = (36x² * 100) / 54x² = 66.67% (Ans.)

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