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
Answer: (c) 200
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=6 = 6x = 6x100 = 600.
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 = 50.
So area of 2 triangles = 2x50 =100.
Area of the square = Side x side = 10 x 10 = 100
Area of three squares = 3x100 =300
So area of one prism = 100+300 = 400
Now area of two shapes = 2x400 = 800
Hence change in area = Area of two shapes - Area of cube
= 800 - 600 =200
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.