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Vlad1618 [11]
3 years ago
11

Will all slices created by a slicing plane that passes through a sphere be the same size

Mathematics
2 answers:
Snowcat [4.5K]3 years ago
6 0

Answer:

The suggestion proposed considering special cases, so that’s what we’ll do.

One special case we could consider is when x=0. If h=r, then we have a hemisphere. You may have learnt that the surface area of a sphere is 4πr2, so the answer in this case is 2πr2. Likewise, we can consider the most extreme cases: when h=2r, we get an area of 4πr2 (the entire sphere), and when h=0, we get zero area.

So if we do manage to get a general formula, we will be able to check it in these special cases.

Another possible idea when x=0 is to consider what happens when h is very small. In this case, the surface area looks a lot like a circle, but the radius of the circle does not seem particularly easy to work out, so maybe we’ll leave this one for a moment. (There are things we can do to approximate the radius using more advanced techniques, but they are currently beyond us.)

Another thing we could consider is the situation where h is very small. Then the part of the sphere between the planes looks very much like the frustum of a cone, and we know how to find the (surface) area of such a shape – see Cones.

If we recall our answer from that problem, we find the formulae for the surface area

π(R+r)s=π(R+r)hcosθ=π(R2−r2)sinθ.

Here, R is the radius of the base of the frustum, r is the radius of the top, h is the perpendicular height, s is the slant length and θ is the angle the slant makes with the vertical.

Step-by-step explanation:

Studentka2010 [4]3 years ago
6 0

Answer: no

Step-by-step explanation:

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ohaa [14]
A general equation to use for this situation is y = mx + b.

For this question, we can assume that y is total cost, m is cost per balloon, x is the amount of balloons, and b as the service fee; so we can set the equation up:

y = (4.50)x + 12

And we can further plug in the total cost to find the number of balloons purchased for the party:

79.50 = (4.50)x + 12

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67.50 = (4.50)x

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5 0
3 years ago
With compound interest, what happens when you start compounding more and more frequently?
VLD [36.1K]
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7 0
3 years ago
The diameter and height of this cylinder are equal to the side length, S, of the cube in which the cylinder is inscribed. What i
sammy [17]

Volume = πr²h

Diameter = S

Height = S

Radius = S/2

Volume = π ( s²/4 ) s

1/4 πs³

The required answer is in the option ( A )

Hope helps!

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3 years ago
Review the attachments. Review the process of solving an equation and fill in the blanks.
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Answer:

1) Combine like terms

2) \sqrt[3]{x} =3

3) cube both sides of the equation

4) 4\sqrt[3]{27} +8\sqrt[3]{27}=36

5) 4(3) + 8(3) = 36

Step-by-step explanation:

1) Combine like terms

2) \sqrt[3]{x} =3

3) cube both sides of the equation

4) 4\sqrt[3]{27} +8\sqrt[3]{27}=36

5) 4(3) + 8(3) = 36

5 0
2 years ago
−3x+5y=2x+3y ordered pairs
NeTakaya

Answer:

y=5/2x

Step-by-step explanation:

5x=2y

y=5/2x

you cant get ordered pairs from this directly you will only get an equation

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