Are these correct:
1a) Find the lateral surface area in square inches of the cone with the following dimensions: h= 24 in, radius = 10 in, slant height = 26 in. (Use Pi= 3.14)
I didn't know how to do:
Lateral Surface Area = ______ square inches (exact answer)
1b) Find the Total surface area in square inches
Total Surface Area= 816.814159 square inches (exact answer)
1c) Volume in cubic inches
Volume = 2513.2741228 cubic inches (exact answer)
1(a) The lateral surface area of a cone is pi R S, where S is the slant height and R is the radius.
Your 1(b) and 1(c) should not be called exact, since you used 3.14 for pi. They can be accurate to three significant figures only. It also appears that you did not include the area of the base in 1(b)
To find the lateral surface area of a cone, you need to use the formula:
Lateral Surface Area = π * r * l
where π is the mathematical constant representing Pi (approximately 3.14), r is the radius of the cone's base, and l is the slant height.
For the given dimensions:
- Radius (r) = 10 inches
- Slant height (l) = 26 inches
Substituting these values into the formula, we get:
Lateral Surface Area = 3.14 * 10 * 26
Calculating this, we find:
Lateral Surface Area = 814.0 square inches (rounding to the nearest whole number)
Therefore, the correct answer for 1a) is 814 square inches.
To find the total surface area of the cone, you need to include the area of the base as well. The formula is:
Total Surface Area = π * r * (r + l)
For the given dimensions, we substitute the values into the formula:
Total Surface Area = 3.14 * 10 * (10 + 26)
Calculating this, we get:
Total Surface Area = 816.8 square inches (rounding to one decimal place)
Therefore, the correct answer for 1b) is 816.8 square inches.
To find the volume of the cone, you can use the formula:
Volume = (1/3) * π * r^2 * h
For the given dimensions, we substitute the values into the formula:
Volume = (1/3) * 3.14 * 10^2 * 24
Calculating this, we find:
Volume = 2513.3 cubic inches (rounding to one decimal place)
Therefore, the correct answer for 1c) is 2513.3 cubic inches.