Answer:
The ratio of the total surface area to the lateral (curved) surface area of the cylinder is 5:3
Step-by-step explanation:
The height of a right circular cylinder is 1.5 times the radius of the base.
Let the radius of base be x
So, Height of a right circular cylinder = 1.5x
Total surface area of cylinder =[tex]2 \pi r h + 2 \pi r^2 = 2 \pi r(h+r)=2 \pi \times x(x+1.5x)=2 \pi \times x \times 2.5x[/tex]
Curved surface area of cylinder = [tex]2 \pi rh = 2 \pi \times x \times 1.5 x[/tex]
So, Ratio of the total surface area to the lateral (curved) surface area of the cylinder = [tex]\frac{2 \pi \times x \times 2.5x}{2 \pi \times x \times 1.5 x}=\frac{2.5}{1.5}=\frac{25}{15}=\frac{5}{3}[/tex]
Hence the ratio of the total surface area to the lateral (curved) surface area of the cylinder is 5:3
