Acone-shaped drinking cup is made from a circular piece of paper of radius r by cutting out a sector and joining the edges ca and cb. find the maximum capacity of such a cup.

The maximum capacity of such cup is

2 × 3.142R^3/9×squareroot3

Explanation:

From the diagram in the attachment,

h= height of the cone, r= radius of the cone,R= radius of the original circular piece of paper

Using pythagorean theorem, we get

r^2+h^2=R^2 => r^2=R^2-h^2

Formular for the volume of a cone is given as V=1/3×(3.142)^2h

Substituting for r^2 when R is a constant

V=1/3(3.142)(R^2-h^2)h

V=1/3(3.142)(R^2-h^3)

V'=0=1/3(3.142)R^2-3h^2)

0=R^2-3h^2

h^2=R^2/3 => h=R/squareroot of 3

V"=1/3(3.142)(0-6)=-2×3.142×h

Negative shows that v is concave

V(R/squareroot of 3)=1/3(3.142)[R^2×R/squareroot 0f 3-(R/squareroot of 3)^3

V=2×3.142×R^3/9× squareroot of 3

  the unit of the measure =

explanation:

  the property that is quantified by the energy needed per of material to raise the temperature by one.

  si unit of energy = joule (j)

  si unit of temperature = kelvin (k)

  si unit of mass of material = kilogram (kg)

the property that is quantified by the energy needed per of material to raise the temperature by one is called specific heat.

the unit of specific heat is

find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2