A balloon has a circumference of 22in. Use the circumference to approximate the surface area of the balloon to the nearset square inch.
possible answers;
154in^2
616in^2
1,521in^2
484in^2
Find the volume of the square pyramid.Round to nearest tenth if necessary.
The pyramid has a base of 24ft. and height of 15ft.
possible answers;
5,184ft^3
1,728ft^3
192ft^3
2,592ft^3
These are the only two problems I haven't been able to figure out. Would someone please help?
Sure, let's start by solving the first problem.
To approximate the surface area of a balloon using its circumference, we can make an assumption that the balloon is a perfect sphere. The formula for the circumference of a circle is given as:
C = 2πr
where C is the circumference and r is the radius of the circle (or in this case, the balloon). Rearranging the formula to solve for the radius, we get:
r = C / (2π)
Plugging in the given circumference of 22 inches, we can calculate the radius:
r = 22 / (2π) ≈ 3.5 inches
Now, to find the surface area of a sphere, we use the formula:
A = 4πr^2
Plugging in the calculated radius, we get:
A = 4π(3.5)^2 ≈ 154 square inches
Therefore, the approximate surface area of the balloon is 154 square inches. So the correct answer for the first question is 154 in^2.
Now, let's move on to the second problem.
The volume of a square pyramid is given by the formula:
V = (1/3) * area of the base * height
For a square pyramid, the area of the base is equal to the side length squared. So we can calculate the volume using the given dimensions:
V = (1/3) * (24^2) * 15
= (1/3) * 576 * 15
= 5760 ft^3
Rounding to the nearest tenth, the volume of the square pyramid is approximately 5760 ft^3. So the correct answer for the second question is 5,760 ft^3.
I hope this helps you with your problems! Let me know if you have any further questions.
Ibelieve the 2nd one is 1,728ft^3, but I do not how to do the balloon.
c = 2pi*r, so r=c/2pi = 11/pi
a = 4pi*r^2 = 4pi(121/pi^2) = 484/pi = 154
v = 1/3 Bh = 1/3 (24^2)(15) = 2880