Step-by-step explanation:
a) is really easy, right ?
the surface area consists of 6 rectangles (as you know, every die has 6 sides). they are 3 pairs of equally sized rectangles.
there are 2 rectangles 7×1, 2 rectangles 7×2, and 2 rectangles 2×1
SA = 2×7×1 + 2×7×2 + 2×2×1 = 14 + 28 + 4 = 46 in²
the volume is just length×width×height
V = 7×2×1 = 14 in³
b)
a little bit more difficult, but with a little trick just as easy.
the surface area consists of the 2 circle areas and the mantle "coating".
the area of a circle is pi×r².
we have to be careful as the given 10 ft is the diameter of these circles. the radius is half of it : 5 ft.
the area of the "mantle" we can calculate by imagining we simply slice it open with one straight line from top to bottom. and then we cut it off the two circles and put it flat on the table.
now we see it is just a rectangle. one side is 12ft. the other is the circumference of the previously attached circles.
circumference of a circle is 2×pi×r
so the surface area is 2×circle + (circumference circle)×12
SA = 2×pi×5² + (2×pi×5)×12 = 50pi + 120pi = 170pi =
≈ 534.07 ft²
the volume is one base area (circle) times height
V = pi×5²×12 = 300pi ≈ 942.48 ft³
