Answer with explanation:
I will illustrate this with the help of few three dimensional shapes.
1. Cylinder
Total Surface area of Cylinder =2π r h + 2 π r²
Base Area= π r² + π r²=2 π r²
Difference between Total surface Area and Base area
=2π r h + 2 π r²- 2 π r²
= 2π r h →→Lateral surface area of cylinder
2. Cone
Total Surface area of Cylinder =π r² + π r l
Base Area= π r²
Difference between Total surface Area and Base area
=π r² + π r l - π r²
= π r l →→Lateral surface Area
In General
→→Total Surface Area of any three dimensional shape= Area of Base + Lateral Surface Area
→Lateral Surface Area=Total Surface Area of any three dimensional shape - Area of Base
≡So, for any three dimensional shape, the difference between the total surface area and base area of any three-dimensional figure is equal to
→→C: Lateral Area
