1. First, let us find the volume. Now the total volume is simply given by adding the volume of the cylinder to that of the hemisphere.
Let us revisit the formulas for the volume of a cylinder and hemisphere.
Cylinder: V = πr^(2)h
Hemisphere: V = (2/3)πr^3
Thus, the total volume is given by πr^(2)h + (2/3)πr^3
Using the values provided in the diagram, we can now say that:
Total volume = π(7)^(2)*10 + (2/3)π(7)^3
= 490π + 686π/3
= 2156π/3 cm cubed
Using π = 22/7, we can now see that:
Total volume = 2156*(22/7) / 3
= 2258.67 cm cubed (to two decimal places)
2. Now let's find the total surface area. Let's review the formulas for total surface area for a cylinder and a hemisphere:
Cylinder: SA = 2πr^2 + 2πrh (this is the area of the top and bottom, plus the area of the rectangle that is wrapped around)
However, since the top of the cylinder is covered by the hemisphere, we don't need to count its area in the surface area, thus we must use SA = πr^2 + 2πrh
Hemisphere: SA = πr^2 + 2πr^2 = 3πr^2 (this is the area of the bottom of the hemisphere plus the area of half of the sphere)
However, since the bottom of the hemisphere is on the cylinder, we don't count this in the total surface area either, therefor we must use SA = 2πr^2
Thus, total surface area is given by:
πr^2 + 2πrh + 2πr^2
= 3πr^2 + 2πrh
Now we can substitute the values of the radius and cylinder height into the formula above. So:
TSA = 3πr^2 + 2πrh
TSA = 3π(7)^2 + 2π(7)(10)
= 147π + 140π
= 287π cm squared
Using π = 22/7, we can now see that:
TSA = 287*(22/7)
= 902 cm squared
