Find the Volume of a sphere if the radius is 3 inches. Leave your answer in terms of π
1 answer:
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We must find the radius so we can plug this into the formula for surface area.
Circumference =
We are going to plug this in as our radius for the most accurate answer.
The surface area of a sphere is
Surface Area =
≈ 451.93 units
Circumference =
We are going to plug this in as our radius for the most accurate answer.
The surface area of a sphere is
Surface Area =
Answer/Step-by-step explanation:
Part A: Net A is the correct net. If we decide to fold the net, we'd get the shape of the prism. Folding back net B won't give us the shape of the prism because of the position and arrangement of the right triangular bases.
Part B:
AB = 3in
BC = 5 in
CD = 9.4 in
Part C: surface area of the prism can be calculated by calculating the area of each part of the net, and summing them together as follows,
Area of the 2 triangular bases = 2(½*base*height of triangle) = 2(½*4*3) = 2*2*3 = 12 in²
Area of the three rectangles =
Surface area of prism = 12 + 112.8 = 124.8 in²
Answer:
114.02 meters
Step-by-step explanation:
The information you're given about the tree will form a triangle, with the three corners being the top of the tree, the point where the tree meets the ground, and the specified point 41.5 meters from the tree. The angle of elevation (70°) is the angle made where the line representing the ground and the line connecting the top of the tree to the ground at the specified point connect.
The angle where the tree meets the ground is 90°, so the triangle a right triangle.
So this all means you know one angle of a right triangle (70°) and the side adjacent to this angle (41.5 meters). You're solving for the height of the tree, which is the side opposite of the angle you know. You can solve using either <em>Sine, Cosine, </em>or <em>Tangent.</em>
Use the acronym SOHCAHTOA to figure out which of those three functions to use. Feel free to look this up for more information if you haven't heard of it before. In this case, we're using Tangent (TOA = Tangent, Opposite side, Adjacent side)
To solve using any of those three functions, you'll need a scientific calculator. On your calculator, you'll see the buttons <em>SIN, COS, </em>and<em>TAN.</em> For this problem, press <em>TAN</em> and you'll see something appear that says <em>tan (___)</em>. You'll need to input a number to get your answer, and here's how to find that number:
Again referencing SOHCAHTOA, the "TOA" part lists Opposite first and then Adjacent. This is because you're going to write a fraction with those two numbers, and since Opposite is first, it's the numerator. That means that Adjacent is the denominator. We don't know the value of the opposite side, so it'll be represented by <em>x</em>, and we do know the value of the adjacent side, 41.5. This means the fraction is .
This isn't the number to input into the calculator -- you need to isolate the variable:
The original equation is:
tan 70 = x/41.5
Multiply both sides by 41.5 (To cancel out the denominator and isolate <em>x</em>)
tan 70 (41.5) = x
Now you've got the equation for <em>x, </em>you're ready to put this in your calculator.
What appeared on your calculator was:
tan(__)
Input like follows:
(tan(70))41.5
The brackets are needed like that so the calculator knows to multiply the entire thing by 41.5. You might get a wrong answer otherwise.
Hit enter, and you'l get the height of the tree:
114.02 meters