Question

Gordon works for a graphic design firm and is creating a label for a food truck vendor. The vendor specializes in finger food and wants to sell food in right conical containers so that they are easy for people to hold. To complete his label, Gordon needs to collect several different measurements to ensure that the label he designs will fit the surface of the container. Gordon has been told that the containers have a diameter of 4 inches and a height of 6 inches.

Answer 1

To find the inside radius of the coffee mug, use the formula for the volume of a cylinder and solve for the radius.

Step-by-step explanation:

To find the inside radius of the coffee mug, we need to use the formula for the volume of a cylinder: V = πr^2h, where V is the volume, r is the radius, and h is the height. We are given the volume of coffee and the depth it is filled to, so we can solve for r as follows:

1. Convert the depth of the coffee to meters (1 cm = 0.01 m).
2. Convert the density of the coffee to kg/m^3 (since the density of water is 1000 kg/m^3).
3. Use the formula V = πr^2h to solve for r.

By following these steps, we can find the inside radius of the coffee mug.

Answer 2

Part A

Find out the slant height of the cone

Applying the Pythagorean Theorem

AC^2=AB^2+BC^2

we have

AC ----> slant height

AB=4/2=2 in

BC=6 in

substitute given values

AC^2=2^2+6^2

AC^2=40

AC=2√10 in

Part B

Find out the measure of the angle formed between the base and the slant height

we have that

tan( by opposite side divided by adjacent side

tan(mm

Part C

see the figure below to better understand the problem

we have that

AC and DC are slant height

triangle ADC is an isosceles triangle

because AC=DC

that means

mmmmthe answer part C is 36.86 degrees