The total surface area of the solid is 4651 sq cm
Step-by-step explanation:
Given,
The diameter of the base = 16 cm
Length of the cylindrical part (h) = 75 cm
The height of the solid = 90 cm
So, the radius of the base(r) = [tex]\frac{16}{2}[/tex] cm = 8 cm
The height of the cone = 90 - 75 cm = 15 cm
The slanting height(l) of the cone = [tex]\sqrt{15^{2}+8^{2} }[/tex] cm = 17 cm [ by Pythagoras theorem]
To find the total surface area of the solid
The solid consists of two separate solids that are a cylinder and a cone.
So, total surface area (TSA) of the solid = TSA of cylinder + TSA of cone
To find the TSA pf cylinder
Formula
TSA of cylinder = 2πrh +2πr
=2πr(r+h)
=2 ×[tex]\frac{22}{7}[/tex]×8×(8+75) sq cm
= 4173.7 sq cm (approx)
Again,
To find the TSA pf cone
Formula
TSA of cone = πrl +2πr
=πr(l+2) sq cm
= [tex]\frac{22}{7}[/tex]×8×(17+2) sq cm
= 477.7 sq cm (approx)
Hence, total surface area (TSA) of the solid = 4173.7 sq cm + 477.7 sq cm
= 4651.4 sq cm
