Question

If a cube is cut by three planes parallel to the>>faces to yeild maximum number of identical>>pieces than what is % increase in the total>>surface area>>(1) 100 % (2) 50 %>>(3) 200 % (4) 150 %​

Answer 1

Answer:

fdtwyryet5ehfgyfbg6t

Answer 2

• The % increase in the total surface area is equal to 100% .

Given :-

• A cube is cut by three planes parallel to the faces to yeild maximum number of identical pieces .

To Find :-

• % increase in the total surface area ?

Concept / Formula used :-

• When n cuts are made(all parallel to the same surface), the cube will be divided into (n + 1) identical cuboidal pieces .
• If cuts are made along the length, breadth and height of cuboidal pieces so formed remains same as initial side of cube .
• Total surface area of cube = 6a² (a = side of cube.)
• Total surface area of cuboid = 2(L•B + B•H + H•L) where L = Length, B = Breadth, H = Height .

Solution :-

Let us assume that, each side of the cube is a unit .

So,

→ Total surface area of cube = 6a² ------ Equation (1)

Now, the cube is cut by three planes parallel to the faces such that, all identical pieces are formed . { That means all three cuts are equidistant from each other . }

So,

→ n = 3

then,

→ Total identical pieces formed = (n + 1) = (3 + 1) = 4

Now, 4 identical cuboidal pieces formed with sides as :-

• One side of the cuboidal piece (along which cuts are made) = (a/4) unit = say Length .
• Other two sides of the cuboidal piece = a unit = say Breadth and Height . { Remains same as the side of the cube . }

So,

→ Total surface area of each cuboidal piece = 2(LB + BH + HL)

→ TSA of each cuboidal piece = 2[(a/4)•a + a•a + a•(a/4)]

→ TSA of each cuboidal piece = 2[(a²/4) + a² + (a²/4)]

→ TSA of each cuboidal piece = 2[(a² + 4a² + a²)/4)

→ TSA of each cuboidal piece = 2•(6a²/4)

→ TSA of each cuboidal piece = 3a²

then,

→ TSA of four cuboidal pieces = 4 × TSA of each cuboidal piece = 4 × 3a² = 12a² ------- Equation (2)

therefore, subtracting Equation (1) from Equation (2) we get,

→ Total surface area increased = TSA of four cuboidal pieces - Total surface area of cube

→ Total surface area increased = 12a² - 6a²

→ Total surface area increased = 6a²

hence,

→ Required % increase in TSA = (Total surface area increased × 100) / Total surface area of cube

→ Required % = (6a² × 100) / 6a²

→ Required % = 100% (Ans.)

∴ Option (1) 100% is correct answer .

Learn more :-

The diagram shows a window made up of a large semicircle and a rectangle

The large semicircle has 4 identical section...

https://brainly.in/question/39998533

a rectangular park is of dimensions 32/3 m ×58/5 m. Two cross roads, each of width 2 1/2 m, run at right angles through ...

https://brainly.in/question/37100173