Let
and
be the respective radii of balloons A and B. If the fixed total volume is V, then
![V = \dfrac{4\pi}3\left({r_A}^3 + {r_B}^3\right)](https://tex.z-dn.net/?f=V%20%3D%20%5Cdfrac%7B4%5Cpi%7D3%5Cleft%28%7Br_A%7D%5E3%20%2B%20%7Br_B%7D%5E3%5Cright%29)
and knowing
and
at the start, we have V = 6916π/3 cm³. Then when
, the radius of the other sphere is
.
Differentiating both sides with respect to time t gives a relation between the rates of change of the radii:
![0 = 4\pi \left({r_A}^2 \dfrac{dr_A}{dt} + {r_B}^2 \dfrac{dr_B}{dt}\right) \implies \dfrac{dr_B}{dt} = -\left(\dfrac{r_A}{r_B}\right)^2 \dfrac{dr_A}{dt}](https://tex.z-dn.net/?f=0%20%3D%204%5Cpi%20%5Cleft%28%7Br_A%7D%5E2%20%5Cdfrac%7Bdr_A%7D%7Bdt%7D%20%2B%20%7Br_B%7D%5E2%20%5Cdfrac%7Bdr_B%7D%7Bdt%7D%5Cright%29%20%5Cimplies%20%5Cdfrac%7Bdr_B%7D%7Bdt%7D%20%3D%20-%5Cleft%28%5Cdfrac%7Br_A%7D%7Br_B%7D%5Cright%29%5E2%20%5Cdfrac%7Bdr_A%7D%7Bdt%7D)
We're given
the whole time. At the moment
, the radius of balloon B is changing at a rate of
![\dfrac{dr_B}{dt} = -\left(\dfrac{12\,\rm cm}{1\,\rm cm}\right)^2 \left(0.1\dfrac{\rm cm}{\rm s}\right) = \boxed{-14.4 \dfrac{\rm cm}{\rm s}}](https://tex.z-dn.net/?f=%5Cdfrac%7Bdr_B%7D%7Bdt%7D%20%3D%20-%5Cleft%28%5Cdfrac%7B12%5C%2C%5Crm%20cm%7D%7B1%5C%2C%5Crm%20cm%7D%5Cright%29%5E2%20%5Cleft%280.1%5Cdfrac%7B%5Crm%20cm%7D%7B%5Crm%20s%7D%5Cright%29%20%3D%20%5Cboxed%7B-14.4%20%5Cdfrac%7B%5Crm%20cm%7D%7B%5Crm%20s%7D%7D)
Answer:
1296 m³
Step-by-step explanation:
Volume = area * height.
Take any of the given faces. I have taken 12m & 12 m.
Area of this face = 1/2 * 12m * 12m
= 72 m²
Height = 18 m.
Thus,
Volume = 72m² * 18m = 1296 m³
Answer:
175/8
Step-by-step explanation:
first 4*2=8 then 8*x=175/8
Answer:
x = 37°
Step-by-step explanation:
the sum of the exterior angles of a convex polygon is 360° so the sum of all the angles must yield to 360°.
just a trial!!!!!
x+2x+x+10+x+18+3x+x-1=360°
9x=333
x= 37°