The formula of a volume of a sphere:

R - radius
We have the volume = 288 in³. Substitute:
![\dfrac{4}{3}\pi R^3=288\qquad\text{multiply both sides by 3}\\\\4\pi R^3=864\qquad\text{divide both sides by}\ 4\pi\\\\R^3=\dfrac{216}{\pi}\to R=\sqrt[3]{\dfrac{216}{\pi}}\\\\R=\dfrac{\sqrt[3]{216}}{\sqrt[3]{\pi}}\\\\R=\dfrac{6}{\sqrt[3]{\pi}}\ in](https://tex.z-dn.net/?f=%5Cdfrac%7B4%7D%7B3%7D%5Cpi%20R%5E3%3D288%5Cqquad%5Ctext%7Bmultiply%20both%20sides%20by%203%7D%5C%5C%5C%5C4%5Cpi%20R%5E3%3D864%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%7D%5C%204%5Cpi%5C%5C%5C%5CR%5E3%3D%5Cdfrac%7B216%7D%7B%5Cpi%7D%5Cto%20R%3D%5Csqrt%5B3%5D%7B%5Cdfrac%7B216%7D%7B%5Cpi%7D%7D%5C%5C%5C%5CR%3D%5Cdfrac%7B%5Csqrt%5B3%5D%7B216%7D%7D%7B%5Csqrt%5B3%5D%7B%5Cpi%7D%7D%5C%5C%5C%5CR%3D%5Cdfrac%7B6%7D%7B%5Csqrt%5B3%5D%7B%5Cpi%7D%7D%5C%20in)
The formula of a surface area of a sphere:

Substitute:
![S.A.=4\pi\left(\dfrac{6}{\sqrt[3]{\pi}}\right)^2=4\pi\cdot\dfrac{6^2}{\sqrt[3]{\pi^2}}=\dfrac{4\pi\cdot36}{\sqrt[3]{\pi^2}}=\dfrac{144\pi}{\sqrt[3]{\pi^2}}\\\\S.A.=\dfrac{144\pi}{\sqrt[3]{\pi^2}}\cdot\dfrac{\sqrt[3]{\pi}}{\sqrt[3]{\pi}}=\dfrac{144\pi\sqrt[3]{\pi}}{\sqrt[3]{\pi^3}}=\dfrac{144\pi\sqrt[3]{\pi}}{\pi}=\boxed{144\sqrt[3]{\pi}\ in^2}](https://tex.z-dn.net/?f=S.A.%3D4%5Cpi%5Cleft%28%5Cdfrac%7B6%7D%7B%5Csqrt%5B3%5D%7B%5Cpi%7D%7D%5Cright%29%5E2%3D4%5Cpi%5Ccdot%5Cdfrac%7B6%5E2%7D%7B%5Csqrt%5B3%5D%7B%5Cpi%5E2%7D%7D%3D%5Cdfrac%7B4%5Cpi%5Ccdot36%7D%7B%5Csqrt%5B3%5D%7B%5Cpi%5E2%7D%7D%3D%5Cdfrac%7B144%5Cpi%7D%7B%5Csqrt%5B3%5D%7B%5Cpi%5E2%7D%7D%5C%5C%5C%5CS.A.%3D%5Cdfrac%7B144%5Cpi%7D%7B%5Csqrt%5B3%5D%7B%5Cpi%5E2%7D%7D%5Ccdot%5Cdfrac%7B%5Csqrt%5B3%5D%7B%5Cpi%7D%7D%7B%5Csqrt%5B3%5D%7B%5Cpi%7D%7D%3D%5Cdfrac%7B144%5Cpi%5Csqrt%5B3%5D%7B%5Cpi%7D%7D%7B%5Csqrt%5B3%5D%7B%5Cpi%5E3%7D%7D%3D%5Cdfrac%7B144%5Cpi%5Csqrt%5B3%5D%7B%5Cpi%7D%7D%7B%5Cpi%7D%3D%5Cboxed%7B144%5Csqrt%5B3%5D%7B%5Cpi%7D%5C%20in%5E2%7D)
Answer:
1
Step-by-step explanation:
divide the volume value by 16
Here we are given that the Alligator's tail length t varies directly as its body length b.
Using this given information and taking k as constant of proportionality, we get this equation :
.................(1)
Now we are given:
body length (b) = 4 feet
tail length (t) = 2.5 feet
plugging these values in equation (1) we have,

from here we can calculate the value of k, dividing both sides by 4
k=2.5/4 = 0.625.............(2)
Now we have to find tail length of alligator if body length is 3.2 feet.
so plugging b=3.2 and k=0.625 in equation (1)

t= 2
So tail length is 2 feet when body length of alligator is 3.2 feet.
Area of the middle rectangular section = length x width = 35 x 20 = 700 square cm.
The radius of the circular sections is 25 cm
Area of a full circle is pi x r^2 = 3.14 x 25^2 = 1962.5 square cm.
There are two quarter circles which is 1/2 of a circle. The area of those would be 1962.5/2 = 981.25 square cm.
Total area of the figure = 700 + 981.25 = 1681.25 square cm
Amount of money Merl has 12000 Yuan
but 1 canadian dollar=6.78 chinese yuan
thus converting amount Merl has to dollars we get:
12000/6.78
=$1,769.91
this implies that the value in Canadian dollars will be $1,769.91