Math, asked by iamarunshetty, 3 months ago

A cube with 10 cm side is cut into two equal halves by a plane passing through its diagonal vertices. How much will be increase in surface area of two shapes over original cube.
(2 Points)

a) 100 cm

b) 10√2 cm

c) 200 cm

d) 200√2 cm

e) 1 meter​

Answers

Answered by ghoshsupratim00
2

Answer: (c) 200 cm^{2}

Step-by-step explanation:

Given that : Length of cube, L=10 cm

To find : Increase in surface area when cube is cut into two equal halves

Area of cube initially, a=6L^{2} = 6x(10)^{2} = 6x100 = 600cm^{3}.

After cutting the cube into two halves through its diagonal vertices, the cube will get split into two triangular prism.

In a triangular prism built from a cube there are two isosceles triangle and three square.

So area of one triangle = 1/2 x base x height

= 1/2 x side x side       [since it is the half of cube]

= 1/2 x 10 x10 = 50cm^{2}.

So area of 2 triangles = 2x50 =100cm^{2}.

Area of the square = Side x side = 10 x 10 = 100cm^{2}

Area of three squares = 3x100 =300cm^{2}

So area of one prism = 100+300 = 400cm^{2}

Now area of two shapes = 2x400 = 800cm^{2}

Hence change in area = Area of two shapes - Area of cube

= 800 - 600 =200cm^{2}

Answered by amitnrw
1

Increase in surface area of two shapes over original cube 200√2 cm² if A cube with 10 cm side is cut into two equal halves by a plane passing through its diagonal vertices.

Solution:

When a cube is cut into two equal halves by a plane passing through its diagonal vertices then two new surface will add.  One on each shape.

One new Surface formed on each new shape will be a rectangle having one side Equal to cube side and another sides as √2.cube side

Side length of cube = 10 cm

Hence rectangle formed will be 10 cm * 10√2 cm

Area of new surface on  each shape = 10 * 10√2 = 100√2 cm²

Area of new Surface on both parts = 2 * 100√2 cm²

= 200√2 cm²

Hence increase in surface area of two shapes over original cube 200√2 cm²

Correct option is d) 200√2 cm²

Note: Units given in options should be in cm² instead of cm.

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