1. A single scoop ice cream cone is made up of a cone filled with ice cream and a half
sphere of ice cream on top of the cone. The cone’s height is double the cone’s diameter.
a. Write an equation for the volume of ice cream in a cone in terms of the radius !.
b. The volume of ice cream is 100 cubic centimeters. What is the radius of the cone?

2.515

Step-by-step explanation:

1. First you add the equation for a cone and a half sphere

(1/3*pi*r^2*h)+(1/2*4/3*pi*r^3)

2. You replace h with 2*r2 because height is 2*Diameter

(1/3*pi*r^2*r2)+(1/2*4/3*pi*r^3)

3. You make the equation equal 100

(1/3*pi*r^2*r2)+(1/2*4/3*pi*r^3)=100

4. Solve for

r=2.515

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

26?

step-by-step explanation: