Hi could you please check my answers?
Find the lateral of the square pyramid (I don't have a picture so I'll describe the figure) the square base is 8m around each side of the square and the slant height is 22m, my answer is 352 cm^2. Am I correct? Plz and thx
Find the surface area of the cone
The diameter of the circle is 8 so the radius is 4 and the slant height is 7 in. My answer is 138.16 in ^2
Ok last one. Volume of a cylinder the diameter us 34 m so it's 17m for the radius and the height is 27m. My answer is 24,501.42m^2. Wow that was a long number. Well thanks to anyone willing to check my answers :)
To find the lateral area of a square pyramid, you need to calculate the area of the four triangular faces. The formula for the lateral area (LA) is LA = (Perimeter of the base) x (Slant height)/2.
In your case, the square base has sides measuring 8m each and the slant height is 22m.
Perimeter of the base = 8m + 8m + 8m + 8m = 32m
LA = (32m) x (22m)/2
= 704m^2
So, the correct answer for the lateral area of the square pyramid is 704 cm^2, not 352 cm^2.
Moving on to the surface area of a cone. The formula for the surface area (SA) of a cone is SA = πr² + πrs, where r is the radius and s is the slant height.
In your case, the radius is 4 inches and the slant height is 7 inches.
SA = π(4 inches)² + π(4 inches)(7 inches)
= 16π + 28π
= 44π
Using the approximation π = 3.142, you can calculate the value:
SA ≈ 44(3.142)
≈ 138.248 square inches
Therefore, the correct answer for the surface area of the cone is approximately 138.25 in², not 138.16 in².
Lastly, for the volume of a cylinder, the formula is V = πr²h, where r is the radius and h is the height.
In your case, the radius is 17m and the height is 27m.
V = π(17m)²(27m)
= 7665π
Using the approximation π = 3.142, you can calculate the value:
V ≈ 7665(3.142)
≈ 24,090.33 cubic meters
Therefore, the correct answer for the volume of the cylinder is approximately 24,090.33 m³, not 24,501.42 m².
Hope this helps! Let me know if you have any further questions.
Sure, let's check your answers one by one!
1. Find the lateral area of the square pyramid with a square base of 8m on each side and a slant height of 22m.
To find the lateral area of a pyramid, you need to calculate the sum of the areas of the four triangular faces. Each triangular face has a base length of 8m (the side length of the square base) and a height equal to the slant height, which is 22m.
Lateral area = 4 * (1/2 * base * height)
= 4 * (1/2 * 8m * 22m)
= 4 * (4 * 22m)
= 352m^2
So, your answer of 352m^2 is correct!
2. Find the surface area of a cone with a diameter of 8 (radius = 4) and a slant height of 7in.
The surface area of a cone consists of the area of the circular base and the lateral or curved surface area. The formula for the lateral surface area of a cone is π * r * l, where r is the radius and l is the slant height.
Lateral surface area = π * r * l
= 3.14 * 4in * 7in
= 87.92in^2 (rounded to 2 decimal places)
The area of the circular base is given by π * r^2, where r is the radius.
Base area = π * r^2
= 3.14 * (4in)^2
= 3.14 * 16in^2
= 50.24in^2
Total surface area = Lateral surface area + Base area
= 87.92in^2 + 50.24in^2
= 138.16in^2
Your answer of 138.16in^2 is correct!
3. Find the volume of a cylinder with a diameter of 34m (radius = 17m) and a height of 27m.
The formula for the volume of a cylinder is π * r^2 * h, where r is the radius and h is the height.
Volume = π * r^2 * h
= 3.14 * (17m)^2 * 27m
= 3.14 * 289m^2 * 27m
= 24,431.98m^3 (rounded to 2 decimal places)
Your answer of 24,501.42m^3 is incorrect. The correct answer is 24,431.98m^3.
I hope this helps! Let me know if you have any further questions.
I agree with all your answers.
For the second one, you included the base.
That's fine, it said nothing about excluding it.
For later questions of this type, if it asks for the "lateral surface area" of a cone, you would exclude the circular base.