Question

To use flat cut outs to form cube cuboids pyramids and cone and to obtain formula for volume and total surface area

Answer 1

First we have to know dimensions of the each 3-D figure.

i) cube:
Measure the edge of the cube.
Let edge = a units
1) Total surface area=(TSA)=6a^2 square units
2) volume =(V)=a^3 cubic units
ii) find dimensions of the cubiod
Let length= l units 
breadth= b units
Height= h units
1) TSA=2(lb+bh+lh)sq units
2) volume=lbh cubic units
iii)measure the slant height =l units
Height =h units 
Base perimeter = p units
Of the pyramid
1)TSA= pl/2 +2×area of the polygon
2) volume=1/3×(base area)×altitude
iv) cone 
Find the dimensions of the cone
Radius = r units
Slant height= l units
Height =h units
1)TSA=curved surface area+base area
=pi×rl+ pi×r^2
=pi×r(l+r) sq units
Where l= sqrt(h^2+r^2)
2) volume=1/3×(base area)×(altitude)
=1/3×pi×r^2×h cubic units