I asked these questions yesterday and thanked whomever helping me before clicking the links. When the links were just google searches, however, they didn't help me seeing as I already did that. The google search calculator doesn't show all steps, and when I tried to plug my numbers in to try to do the problem myself, it never worked. So, real help would be nice :)
Find the lateral area of the square triangle. Show all steps.
Base: 8m
Height: 22m
Find the surface area of the cone. Use 3.14 for pi. Show all steps.
Diameter: 8in
Height: 7in
Find the volume of the cylinder. Use 3.14 for pi. Show all steps.
Diameter: 34m
Height: 27m
Thanks~!
First of all, since you switched your name to "Frustrated Further" I have no way of finding your previous post.
Secondly, your first question asks for "the lateral area of the square triangle". This makes no sense.
2nd question:
The lateral surface area of a cone is πrs, where r is the radius and s is the slant height.
s^2 = 4^2 + 7^2 = 65
s = √65
area = π(4)√65 inches^2 = .....
3rd:
Volume of cyliner = π r^2 h
= π(17)^2 (27)
= 7803π m^3
Thank you! My first one not making sense would explain my endless frustration, but it says.
Find the lateral area of the square pyramid. Show all steps.
The square triangle is laying on its side, with an 8m next to the square's base and another 8m on the inside next to the square's base. There is then a 22m pointing to the dotted line marking the middle up the triangle.
I hope this makes sense?
"The square triangle" ????
So I conclude that you have a square pyramid , and you want the area of the 4 triangles.
Let's look at one of them
We know its base of 8m
We need its height.
This height is the hypotenuse of a right-angled triangle formed from the height of the pyramid and the distance from the centre to the edge (4 m)
so s^2 = 4^2 + 22^2 = 500
s = √500
so the area of the 4 triangles
= 4 (1/2)base * height
= 2(4)√500
= 8 * √100 * √5
= 80√5 m^2
= ....
Hmm. When you say
There is then a 22m pointing to the dotted line marking the middle up the triangle.
it sounds like the triangle has a base of 8 and an altitude of 22. So, its area would be
8*22/2
The area of the cone is:
A=3.14*r*(r+sqrt(r^2+h^2))
Here: r=4
h=sqrt(7^2-4^2)=sqrt(33)
A=3.14*4*(4+sqrt(16+33))=3.14*4*11=132*3.14=414.48 inches squared
I apologize if the previous response wasn't helpful. Let's go through each question step by step and find the answers together.
1. To find the lateral area of a square triangle, we'll first calculate the length of the hypotenuse. Since it's a right-angled triangle, we can use the Pythagorean theorem: c^2 = a^2 + b^2, where c is the hypotenuse and a, b are the other two sides. In this case, the base is 8m and the height is 22m.
Using the formula:
c^2 = 8^2 + 22^2,
c^2 = 64 + 484,
c^2 = 548.
Taking the square root of both sides, we get:
c ≈ sqrt(548),
c ≈ 23.41m (rounded to two decimal places).
Now that we have the hypotenuse, we can find the lateral area. The lateral area of a triangular shape is given by the formula: Lateral Area = (Perimeter / 2) * Height. In this case, the base is the hypotenuse (23.41m) and the height is 22m.
Using the formula:
Lateral Area = (23.41 / 2) * 22,
Lateral Area ≈ 257.55m^2 (rounded to two decimal places).
Therefore, the lateral area of the square triangle is approximately 257.55 square meters.
2. To find the surface area of a cone, we need to calculate the area of the base and the lateral area separately. The formula for the base area of a cone is A = πr^2, where r is the radius. In this case, the diameter is given as 8in, so the radius is 8in / 2 = 4in.
Using the formula:
Base Area = π * (4in)^2,
Base Area ≈ 50.24in^2 (rounded to two decimal places).
Next, let's calculate the lateral area of the cone. The formula for the lateral area of a cone is Lateral Area = πr * l, where l is the slant height. To find the slant height, we can use the Pythagorean theorem: l^2 = r^2 + h^2, where h is the height of the cone (7in) and r is the radius (4in).
Using the formula:
l^2 = (4in)^2 + (7in)^2,
l^2 = 16in^2 + 49in^2,
l^2 = 65in^2.
Taking the square root of both sides, we get:
l ≈ sqrt(65),
l ≈ 8.06in (rounded to two decimal places).
Now that we have the slant height, we can find the lateral area. Using the formula:
Lateral Area = π * 4in * 8.06in,
Lateral Area ≈ 101.74in^2 (rounded to two decimal places).
Finally, to find the surface area of the cone, we add the base area and the lateral area together:
Surface Area = Base Area + Lateral Area,
Surface Area ≈ 50.24in^2 + 101.74in^2,
Surface Area ≈ 151.98in^2 (rounded to two decimal places).
Therefore, the surface area of the cone is approximately 151.98 square inches.
3. To find the volume of a cylinder, we use the formula Volume = πr^2h, where r is the radius and h is the height. In this case, the diameter is given as 34m, so the radius is 34m / 2 = 17m.
Using the formula:
Volume = π * (17m)^2 * 27m,
Volume ≈ 15,660m^3 (rounded to two decimal places).
Therefore, the volume of the cylinder is approximately 15,660 cubic meters.
I hope this explanation was helpful. Let me know if you have any further questions!