The spherical balloon is inflated at the rate of 10 m³/sec. Find the rate at which the surface area is increasing when the radius of the sphere is 3m?

The balloon has a volume dependent on its radius :

Differentiating with respect to time gives

If the volume is increasing at a rate of 10 cubic m/s, then at the moment the radius is 3 m, it is increasing at a rate of

The surface area of the balloon is

and differentiating gives

so that at the moment the radius is 3 m, its area is increasing at a rate of

Related Questions

What is 4.1 equal as a fraction.

41/10 it is as a fraction

The area of a rectangle is 180 squared in2. The ratio of the length to the width is 5 : 4Find the length and the width. The length of the rectangle is nothing in.

180 in² - the area

width × lenght - the area

length : width = 5 : 4 therefore length = 5x and width = 4x

(x - some unit of length)

The equation:

(5x)(4x) = 180

20x² = 180     divide both sides by 20

x² = 9 → x = √9 → x = 3 in.

5x = 5(3 in) = 15in

Which one is greater 8.3 or 8.03

Number 8.3 is greater than 8 .03.

Step-by-step explanation:

Given  : 8.3 or 8.03.

To find : Which one is greater.

Solution : We have given  8.3 or 8.03.

In 8.3

We can see Ones place is 8 and tenth place digit is 3.

In 8.03

Ones place is same 8 but the tenth place digit is 0 .

So, the number 8.3 is greater than 8 .03.

Therefore, Number 8.3 is greater than 8 .03.

8.3 because .3 is in the tenths place but .03 is in the hundredths place, which is smaller.

PLEASE HELP! THANKS! The measures, in degrees, of the 3 angles of a triangle are given by 2x +1, 3x - 3, and 9x.
What is the measure of the smallest angle?

A.) 13 degrees
B.) 27 degrees
C.) 36 degrees
D.) 117 degrees

please show how to solve this I GIVE THANKS!!!