Question

Total surface area and volume derivation of using flat cutouts

Answer 1

Answer:

Flat Cutouts is a way of making a 3 – d figure represent in 3 – d by cutting different shapes it is made of.

(i) Cube

Each Cube consists of 6 squares with equal sides

The figure above shows the flat cutouts of Cube.

Now Total Surface Area = Area of 6 squares = 6 a2  

Where a = side of square.

For Volume, we will multiply the Area with the height of the surface = a2 × a = a3

(ii) Cuboid

Each Cuboid Consists of 6 rectangles having 3 dimensions namely length, breadth and height.

Now Total Surface Area of Cuboid = Area of all rectangles above = 2 lb + 2 bh + 2 hl

Total Surface Area = 2(lb + bh + hl)

Where, l = length, b = breadth and h = height

And Volume = Area of Rectangle × height

Volume = (l b) × h  

The volume of Cuboid = lbh

(iii) Pyramid

Total Surface Area = Area of Four Triangles + Area of Square

Total Surface Area = 1/2 h a + 4 a

(where h = height of Pyramid and a = side of base)

Volume of Pyramid = Area of Base × 1/3 height

Volume of Pyramid = 1/3 a2 h

Explanation: