Question

A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total volume of the solid is 18 cubic centimeters. Find the radius of the cylinder that produces the minimum surface area. (Round your answer to three decimal places.)

Answer 1

The radius of the cylinder that produces the minimum surface area is 1.62 cm

For given question,

A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder.

We have the formulas for the volume of the sphere and the cylinder:

Vs = (4/3) × π × r³

Vc = π × h × r²

where, Vs is the volume of the sphere

Vc is the volume of the cylinder

Thus the total volume of the solid would be,

(4/3) × π × r³ + π × h × r² = 18

Now, the formula for the surface area of the cylinder and sphere are:

As = 4 × π × r²

Ac = 2 × π × r × h + 2 × π × r²

Using this equation for the total surface area of the solid, we can see that as "h" increases, so will the surface area.

Therefore, the smallest surface area will occur at h = 0.

Thus:

⇒ (4/3) × π × r³ + π × 0 × r² = 18

⇒ (4/3) × π × r³ = 18

⇒  r³ = 4.28

⇒ r = 1.62

Therefore, the radius of the cylinder that produces the minimum surface area is 1.62 cm

Learn more about the cylinder here:

brainly.com/question/17063223

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