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Q:A rectangular box has the dimensions 12 in x10in x8in. What is the largest possible volume of a right circular cylinder that is placed inside the box?

Can someone please provide detailed explanation for this problem?

Q:A rectangular box has the dimensions 12 in x10in x8in. What is the largest possible volume of a right circular cylinder that is placed inside the box?

Can someone please provide detailed explanation for this problem?

volume = pi*r^2*h when radius is max then volume will be max so in this we can have 10in as diameter so radius will be 5in. then height will be 8in so vol = 200pi

As all the dimensions are different. So. the key here is to find the maximum radius the circular faces. In this case if the cylinder is placed in vertical position with height = 8 and radius = 10/2 then the area will be maximux = 200pi.

We cant take longest side as diameter because of different dimensions. So, 360pi is ruled out.

We cant take 8 in as the diameter, well in that case area = 192pi. _________________

As all the dimensions are different. So. the key here is to find the maximum radius the circular faces. In this case if the cylinder is placed in vertical position with height = 8 and radius = 10/2 then the area will be maximum = 200pi.

We cant take longest side as diameter because of different dimensions. So, 360pi is ruled out.

We cant take 8 in as the diameter, well in that case area = 192pi. _________________

As all the dimensions are different. So. the key here is to find the maximum radius the circular faces. In this case if the cylinder is placed in vertical position with height = 8 and radius = 10/2 then the area will be maximux = 200pi.

"We cant take longest side as diameter because of different dimensions. So, 360pi is ruled out."

We cant take 8 in as the diameter, well in that case area = 192pi.

"[color=#BF0000]We cant take longest side as diameter because of different dimensions. So, 360pi is ruled out."[/color]

Why can't we take the largest side as diameter (r=6) in this case is my question? Please explain.

See, if you take r=6 (diameter = 12) then try to think of the circular surface of the cylinder. The width of the cuboid = 10. Cylinder will not have the complete circular surface. See the attached diagram.

See, if you take r=6 (diameter = 12) then try to think of the circular surface of the cylinder. The width of the cuboid = 10. Cylinder will not have the complete circular surface. See the attached diagram.