# math question, not sure how to categorise it sorry (1 Viewer)

#### Kaatie

##### Member
A spherical balloon is expanding so that the radius increase at the rate of 0.5cm/sec. Find, the rate at which the surface area is increase when the radius is 24cm. Leave your answer in terms of pi.

and secondly: a cube has three sides painted blue, two sides painted red and one side painted green. The cube is rolled onto a flat table. What is the probability that at least one blue side will be at right angles to the surface of the table. How are you supposed to know what order the colours are in. there could be many different ways? right angles to the table means the blue would be on the side right?

thanks guys

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#### -tal-

##### Member
A spherical balloon is expanding so that the radius increase at the rate of 0.5cm/sec. Find, the rate at which the surface area is increase when the radius is 24cm. Leave your answer in terms of pi.
dr/dt = 0.5cm/s

SA of Sphere = 4(pi)r2

dA/dr = 8(pi)r

dA/dt = dA/dr x dr/dt
= 8(pi)rx 0.5
= 4(pi)r

r=24, dA/dt = 96pi

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#### ComingUpForAir

##### Banned
and secondly: a cube has three sides painted blue, two sides painted red and one side painted green. The cube is rolled onto a flat table. What is the probability that at least one blue side will be at right angles to the surface of the table. How are you supposed to know what order the colours are in. there could be many different ways? right angles to the table means the blue would be on the side right?
When it says 'right-angles' it means any side excluding the very top face (i.e what you'd see from birds-eye view) and the very bottowm face (i.e. the face you cant see). So at any given time the cube will have 4 faces at right angles with the table (i.e a 2/3 chance), then you account for the condition that those faces have to be blue.

Yea and the first question you asked is a 'related rate' (if you wanted to 'catagorise it.)

#### Cloesd

##### Member
When it says 'right-angles' it means any side excluding the very top face (i.e what you'd see from birds-eye view) and the very bottowm face (i.e. the face you cant see). So at any given time the cube will have 4 faces at right angles with the table (i.e a 2/3 chance), then you account for the condition that those faces have to be blue.

Yea and the first question you asked is a 'related rate' (if you wanted to 'categorize it.)
Interesting cube question.

The probability is 1, there is no way to way to get a cube with 3 blue sides to ever land in a way where one of those sides is NOT perpendicular to the table.

#### Cloesd

##### Member
Let me elaborate, a cube has six faces. At any time only two of these sides can be NOT perpendicular to the table. But there are 3 blue sides, of which only 2 can be NOT perpendicular to the table. Thus, at least 1 blue side will always be perpendicular to the table face, regardless of arrangement.