Surface area
Let's calculate the surface area of the rectangular block. It has length, width and height of L = 15, W = 5, H = 8. The surface area is going to be
SA = 2*(LW+WH+LH)
SA = 2*(15*5+5*8+15*8)
SA = 470
This is without the cylinder attached to the top surface. If we account for that, then we'll have to subtract off the area of the circle covered up which is
pi*r^2 = pi*3^2 = 9pi = 28.27433 approximately
So 470-28.27433 = 441.72567 is the approximate surface area of the rectangular block after we subtract off the circular portion covered up by the cylinder.
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The lateral surface area of the cylinder is approximately
2*pi*r*h = 2*pi*3*4 = 24pi = 75.39822
Which adds onto the top circular area of 28.27433 to get 28.27433+75.39822 = 103.67255
Meaning that 103.67255 is the surface area for the cylinder portion. Again we don't worry about the bottom portion as it's not part of the outer surface.
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Overall, the total surface area of this compound 3D figure is
(surface area for rectangular portion) + (surface area cylinder portion) = 441.72567+103.67255 = 545.39822
When rounding to the nearest whole number, the total surface area is about 545 square cm
<h3>Answer: 545 square cm</h3>
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Volume
The rectangular block has volume L*W*H = 15*5*8 = 600 cubic cm
The cylinder has volume pi*r^2*h = pi*3^2*4 = 113.0973355 approximately
Add the two volumes to get 600+113.0973355 = 713.0973355 and this rounds to 713. We don't have to do any subtraction in this section.
<h3>Answer: 713 cubic cm</h3>
