A solid cube has sides of length 4 cm. A hemisphere of radius 1.5 cm is removed from the cube. Calculate the total surface area, in cm^2 to 3 significant figures, of the remaining solid.
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Five sides of the cube are unaffected; their surface
area is 5 x 4^2 = 80cm^2
The sixth surface has a flat part with a "dent" in the middle.
The area of the flat part is 4^2 - pi(1.5)^2
= 8.93142
The surface area of the "dent" is 2pi(1.5)^2 (half the area of a sphere)
= 14.13717
So the total surface area is
80 + 8.93142 + 14.13717 = 103.069cm^2
area is 5 x 4^2 = 80cm^2
The sixth surface has a flat part with a "dent" in the middle.
The area of the flat part is 4^2 - pi(1.5)^2
= 8.93142
The surface area of the "dent" is 2pi(1.5)^2 (half the area of a sphere)
= 14.13717
So the total surface area is
80 + 8.93142 + 14.13717 = 103.069cm^2