Please provide the detailed information on how to derive the formula of the total surface area and volume for Cone, Cube, Cubiod and Pyramid using flat cut outs. 
Thank you

Asked by PRARTHANA R | 21st May, 2014, 11:57: AM

Expert Answer:

Let us derive the total surface area of the cone, with radius 'r', and slant height 's'.
Cut the cone along the axis.
Thus, the shaded portion is the part of the circle, with radius 's'.
The area of the above circle is therefore,pi s squared
The circumference of the larger circle is 2 pi s
The circumference of the base circle with radius r is 2 pi r.
The ratio of area of the shaded sector to the area of the whole circle, is the same as the ratio of the arc AB to circumference of the whole circle.
fraction numerator A over denominator pi s squared end fraction equals fraction numerator 2 pi r over denominator 2 pi s end fraction rightwards double arrow A equals pi r s
Thus the total surface area of the cone = Curved surface area of the cone + Base area of the cone
T o t a l space s u r f a c e space a r e a space o f space t h e space c o n e equals pi r s plus pi r squared space s q u a r e space u n i t s
The formula for the volume of the cone can be derived using integration and that is not in 10th standard syllabus.

Answered by Vimala Ramamurthy | 27th May, 2014, 02:09: PM

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