The ratio of the volumes of a right circular cylinder and a sphere is

1.	The ratio of the volumes of a right circular cylinder and a sphere is 3 ∶ 2. If the radius of the sphere is double the radius of the base of the cylinder; find the ratio of the surface areas of the cylinder and the sphere? 1). 2 ∶ 12). 3 ∶ 13). 1 ∶ 2 4). 4 ∶ 1
Answer» LET RADIUS of cylinder be r and radius of sphere be R Volume of a right CIRCULAR cylinder = πr²h Volume of a sphere = (4/3)πR³ Given, R = 2r Ratio of the volumes of a right circular cylinder and a sphere is 3 : 2 $(\Rightarrow \;\FRAC{{\pi {r^2}h}}{{\frac{4}{3}\pi {R^3}}}\; = \;\frac{3}{2})$ ⇒ h = 16r Curved Surface area of a right circular cylinder = 2πrh Surface area of the sphere = 4πR² ∴ Ratio of the surface areas of the cylinder and the sphere $(= \;\frac{{2\pi rh}}{{4\pi {R^2}}}\; = \;\frac{{32{r^2}}}{{4 \times 4{R^2}}}\; = \;2\;:\;1)$

The ratio of the volumes of a right circular cylinder and a sphere is 3 ∶ 2. If the radius of the sphere is double the radius of the base of the cylinder; find the ratio of the surface areas of the cylinder and the sphere? 1). 2 ∶ 12). 3 ∶ 13). 1 ∶ 2 4). 4 ∶ 1

Answer»

LET RADIUS of cylinder be r and radius of sphere be R

Volume of a right CIRCULAR cylinder = πr²h

Volume of a sphere = (4/3)πR³

Given,

R = 2r

Ratio of the volumes of a right circular cylinder and a sphere is 3 : 2

$(\Rightarrow \;\FRAC{{\pi {r^2}h}}{{\frac{4}{3}\pi {R^3}}}\; = \;\frac{3}{2})$

⇒ h = 16r

Curved Surface area of a right circular cylinder = 2πrh

Surface area of the sphere = 4πR²

∴ Ratio of the surface areas of the cylinder and the sphere $(= \;\frac{{2\pi rh}}{{4\pi {R^2}}}\; = \;\frac{{32{r^2}}}{{4 \times 4{R^2}}}\; = \;2\;:\;1)$

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