Step-by-step explanation:
this is again a combined object.
at the bottom there is a cylinder.
and on top there is half of a sphere (I assume it is a sphere, because there is no additional information about its height, and we could therefore not solve this otherwise).
for the total volume we need to calculate both volumes and add these results.
for the total surface area we need to calculate both surface areas, but remove the top surface area of the cylinder, because the half-sphere is covering it.
so, let's start with the volume :
the volume is a cylinder is
ground area × height = pi×r² × height
the radius is half of the diameter, so, r = 18/2 = 9 ft.
in our case that gives us
pi×9² × 10 = pi×81 × 10 = 810×pi = 2,544.690049... ft³ ≈
≈ 2,544.7 ft³
the volume of a sphere is
pi×r³ × 4/3
and of a half-sphere therefore
pi×r³ × 4/3 / 2 = pi×r³ × 2/3 = pi×9³ × 2/3 = pi×9² × 2 =
= pi×81 × 2 = 162×pi = 508.9380099... ft³
≈ 508.9 ft³
the total volume is then
3,053.628059... ft³ ≈ 3,053.6 ft³
the surface area :
the surface area of a cylinder is
the areas of the circles on the top and the bottom (but here we need only the bottom) plus the area of the lateral side area, the "mantle", which is the circumference of the basic circle times height.
so, in our case we get
pi×r² + 2×pi×r×height
pi×9² + 2×pi×9×10 = 81pi + 180pi = 261pi =
= 819.9556826... ft² ≈ 820 ft²
the surface area of a sphere is
4×pi×r²
and therefore if a half-sphere
4×pi×r² / 2 = 2×pi×r²
in our case
2×pi×9² = 2×pi×81 = 162pi = 508.9380099... ft²
≈ 508.9 ft²
the total surface area is then
1,328.893692... ft² ≈ 1,328.9 ft²
