Sage-Tips

How do you find the least surface area given the volume?

Presumably you are asked to find the minimum surface area given the volume V. V = L*W*H where L, W, H are the length, width, and height of the box. To minimize the surface area we set the partial derivatives dS/dx, dS/dy to zero i.e. The minimum surface area = 6*V^(2/3) where V is the volume of the box.

How is surface area calculated?

Surface area is the sum of the areas of all faces (or surfaces) on a 3D shape. To find the surface area of a cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the surface area.

How do you find the surface area when given the volume of a rectangle?

Formulas for a rectangular prism:

1. Volume of Rectangular Prism: V = lwh.
2. Surface Area of Rectangular Prism: S = 2(lw + lh + wh)
3. Space Diagonal of Rectangular Prism: (similar to the distance between 2 points) d = √(l2 + w2 + h2)

How do you find the length and width of a cuboid given the volume?

Therefore, the volume of the cuboid is 120 cm3.

1. Calculating the Length of a cuboid when Volume, Width and Height are Given. The formula is l = V / (w)(h)
2. Calculating the Width of a cuboid when Volume, Length and Height are Given.
3. Calculating the Height of a cuboid when Volume, Length and Width are Given.

How do you find the minimum surface area of a cylinder?

Determine the minimum surface area. The answer is 96 π. Volume of Cylinder, V = π r 2 h = 128 π (eq1) Surface Area of Cylinder, S A = 2 π (r 2 + r h) (eq2)

How do you find the maximum value of a cubic polynomial?

Maximizing the volume of the box leads to finding the maximum value of a cubic polynomial. Watch a video about optimizing the volume of a box. Suppose the dimensions of the cardboard in (Figure) are 20 in. by 30 in.

How do you maximize the volume of an open-top box?

Now let’s apply this strategy to maximize the volume of an open-top box given a constraint on the amount of material to be used. An open-top box is to be made from a 24 in. by 36 in. piece of cardboard by removing a square from each corner of the box and folding up the flaps on each side.

How do you find the area of 125 with one critical point?

So, let’s get the derivative and find the critical points. Setting this equal to zero and solving gives a lone critical point of y = 125 y = 125. Plugging this into the area gives an area of A ( 125) = 31250 f t 2 A ( 125) = 31250 f t 2.