Are these correct
2a) For the cone, find the Lateral Surface Area in square inches. (Hint: Use the pythagorean theorem to find the slant height)
diameter= 12 inches, height= 8 inches
Lateral Surface Area= 301.5928 square inches
2b) Find the volume in cubic inches
Volume = 88.49555 cubic inches
You included the area of the circular base.
I understood that "lateral surface area" excluded the base of the solid.
For the volume I got pi(6^2)(8)/3 = 301.5929
mmmmh, now would that be a coincidence that this answer is the same as the one you got for the total surface area???
so its the same???
no, just a simple coincidence with those numbers.
I tried it with a cone of height 12 and radius 5, resulting in a slant height of 13
the total surface area would be 65pi + 25pi = 90pi and
the volume would be 25pi(12)/3 = 100pi
All we need in one exception to our perceived relationship and it is pooched.
To check if the given answers for 2a and 2b are correct, we can calculate them step-by-step using the formulas for lateral surface area and volume of a cone.
For 2a) finding the lateral surface area:
The formula for the lateral surface area of a cone is:
Lateral Surface Area = πr * slant height
Given:
Diameter = 12 inches, radius = diameter/2 = 12/2 = 6 inches
Height = 8 inches
To find the slant height, we can use the Pythagorean theorem:
Slant height^2 = height^2 + radius^2
Plugging in the values:
Slant height^2 = 8^2 + 6^2
Slant height^2 = 64 + 36
Slant height^2 = 100
Slant height = √100 = 10 inches
Now we can calculate the lateral surface area:
Lateral Surface Area = π * radius * slant height
Lateral Surface Area = 3.14159 * 6 * 10
Lateral Surface Area ≈ 188.49856 square inches
So, the correct answer for 2a) is approximately 188.49856 square inches, which is different from the given answer.
For 2b) finding the volume:
The formula for the volume of a cone is:
Volume = (1/3) * πr^2 * height
Given:
Radius = 6 inches
Height = 8 inches
Now we can calculate the volume:
Volume = (1/3) * 3.14159 * 6^2 * 8
Volume ≈ 301.592894 cubic inches
So, the correct answer for 2b) is approximately 301.592894 cubic inches, which is different from the given answer.
Therefore, the given answers for both 2a) and 2b) are incorrect.