Use differentials to estimate the amount of material in a closed cylindrical can that is 50 cm high and 20 cm in diameter if the metal in the top and bottom is 0.2 cm thick, and the metal in the sides is 0.05 cm thick.

The amount of material in a closed cylindrical is 282.6 cm³.

Step-by-step explanation:

Given : A closed cylindrical can that is 50 cm high and 20 cm in diameter if the metal in the top and bottom is 0.2 cm thick, and the metal in the sides is 0.05 cm thick.

To find : Use differentials to estimate the amount of material in a closed cylindrical ?

Solution :

Let r and h be the radius and base of the cylinder.

The volume of the cylinder is V=\pi r ^2 h

Differentiate the volume,

i.e.

Since, the metal in the top and bottom is 0.2 cm thick, and the metal in the sides is 0.05 cm thick.

Increase in radius dr=0.05

Increase in height of cylinder is dh=0.2+0.2=0.4

Diameter d= 20 cm

Radius r=10 cm

Height h= 50 cm

Substitute the values,

Therefore, the amount of material in a closed cylindrical is 282.6 cm³.

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .

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step-by-step explanation: