The base radius of an ice cream cone is 3.5 cm and the slant height is 6.5 cm. what is the capicity of the ice cream cone and it’s surface area?

The capacity of the cone is 70.26 cubic cm.

The surface area of cone is 109.96 square cm.

Step-by-step explanation:

We have been given that the base radius of an ice-cream cone is 3.5 cm and the slant height is 6.5 cm.

The capacity of the ice cream cone will be equal to volume of cone.

First of all, we will find height of our given cone using Pythagoras theorem.

, where,

h = Height of cone,

l = Slant height of cone,

r = Radius of cone.

Upon substituting our given values in volume formula we will get,

Therefore, the capacity of the cone is 70.26 cubic cm.

Upon substituting our given values in surface area formula we will get,

Therefore, the surface area of cone is 109.96 square cm.

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3