Step-by-step explanation:
the volume of any pyramid is
base area × height / 3
so, since we know the base area (a square with 23 mm side length), the only trick we need to do is to get the inner height (straight up in the middle from the base area to the top of the pyramid).
because this is a regular pyramid (the top of the pyramid is right above the middle of the base area), we can use Pythagoras for right-angled triangles
c² = a² + b²
with c being the Hypotenuse (the baseline of the triangle opposite of the 90° angle) and in our case the outer height along a side area triangle (24 mm).
the legs of that right-angled triangle are half of a base area side length (remember, the top of the pyramid is right over the middle of the base area square) and the inner height to the top.
so, we have
24² = 12.5² + height²
height² = 24² - 12.5² = 576 - 156.25 = 419.75
height = 20.48780125... mm
so, the volume of the pyramid is then
23² × 20.48780125... / 3 = 3,612.682287... mm³ ≈
≈ 3,612.7 mm³
- Triangle Inequality Theorem: States that the sum of any two sides of a triangle is greater than the length of the third side;
So for this, we are applying the triangle inequality theorem. If any of the inequalities are not true, then this cannot be a triangle. (Let A = 7.7, B = 4.0, and C = 1.7)
<u>Since the second inequality is false, these lengths cannot form a triangle.</u>
9514 1404 393
Answer:
1816.7 in³ ≈ 29,769.6 cm³
Step-by-step explanation:
The surface area of a sphere is given by the formula ...
A = 4πr²
Then the radius is ...
r = √(A/4π) = (1/2)√(A/π)
The volume of a sphere is given by the formula ...
V = 4/3πr³
Using the above value of r, we find the volume to be ...
V = (4/3)π(1/2)³(A/π)^(3/2) = 1/6√(A³/π) ≈ 1816.7 in³
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The answer is requested in cm³. The conversion factor is (2.54 cm/(1 in))³, so this volume is ...
(1816.7 in³)·(2.54 cm/(1 in))³ = 29,769.6 cm³
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<em>Additional comment</em>
We suspect an error in the problem statement, as the given units are square inches and the requested volume is in cubic centimeters. Usually, there would be an explicit statement regarding the necessity for units conversion.
14x is the difference between 23x and 9x.
