Respuesta :
Answer:
The radius of cylinder is 1.05 cm and
The height of cylinder is 2.11 cm
Step-by-step explanation:
Given as :
The total surface area of cylinder = 21 cm
The curved surface area of cylinder = [tex]\frac{2}{3}[/tex] of the total surface area
I.e The curved surface area of cylinder = [tex]\frac{2}{3}[/tex] × 21 = 14 cm
∵ The total surface area of cylinder = 2 [tex]\pi[/tex] r h + 2 [tex]\pi[/tex] r²
Where r is the radius and h is the height of cylinder
Or, 2 [tex]\pi[/tex] r h + 2 [tex]\pi[/tex] r² = 21 cm
Or, [tex](2\times \Pi \times r\times h) + (2\times \Pi\times r^{2} )[/tex] = 21 cm ....a
Again ∵ The curved surface area of cylinder = 2 [tex]\pi[/tex] r h
Where r is the radius and h is the height of cylinder
Or, 2 [tex]\pi[/tex] r h = 14 cm . ...b
so . put the value of a into b
I.e 14 cm + [tex](2\times \Pi\times r^{2} )[/tex] = 21 cm
Or, [tex](2\times \Pi\times r^{2} )[/tex] = 21 cm - 14 cm
Or, [tex](2\times \Pi\times r^{2} )[/tex] = 7
so , r² = [tex]\frac{7}{2\pi }[/tex]
∴ r² = [tex]\frac{49}{44}[/tex]
I.e r = [tex]\sqrt{\frac{49}{44} }[/tex]
So, radius = [tex]\frac{7}{\sqrt{44} }[/tex] cm
or, r = 1.05 cm
Put the value of r in eq b
2 [tex]\pi[/tex] r h = 14 cm
Or, 2 [tex]\pi[/tex] × [tex]\frac{7}{\sqrt{44} }[/tex] × h = 14 cm
So, h = [tex]\frac{\sqrt{44} }{\pi }[/tex]
Or, h = 2.11 cm
Hence The radius of cylinder is 1.05 cm and The height of cylinder is 2.11 cm Answer
