First step: You have to know which geometric shapes' dimensions can be calculated given only the volume:
They are hemisphere and sphere.
Now you have to determine which shape is the two figures. To do this, you have to calculate the dimensions of the first figure given that it is a hemisphere, and then calculate it again given that the first figure is a sphere. Do the same step for the second figure.
Second Step: After you have written down your four equations (remember to label them). Now you can determine which shape is the two figures. Now you will apply the rules of calculating the surface area on the 2 equations for the second figure (because it has a larger volume than the first figure, therefore it must be the larger figure), and see which equation match up to the given surface area: 192mm^2.
Third Step: So now after you have matched up the surface area, you'd know which shape is the two figures. Using the calculated dimensions in Step 1 for that geometric shape, calculate the surface area of the remaining figure.
Working out:
First figure:
find the radius (sphere).
(4/3)πr^3= V
(4/3)πr^3=343
πr^3=343/(4/3)
r^3=257.25/π
r= 3^√257.25
r= 4.342 mm
Find the surface area (sphere)
A= 4πr^2
A= 236.91
Find the radius (hemisphere).
(2/3)πr^3= 343
πr^3= 343/(2/3)
r^3= 257.25/π
r= 3^√81.885
r= 5.471
Surface area.
2πr^2= A
2πr^2= 188.077
Second figure:
Find the volume (sphere).
(4/3)πr^3= V
(4/3)πr^3= 512mm^3
πr^3= 512/(4/3)
r^3= 384/r^3
r= 3^√122.23
r= 4.962
Find the surface area (sphere)
A= 309.502 mm^2
Find the radius (hemisphere)
r= 6.252 mm
Find the surface area.
A = 245.652 mm^2
