Answer:
22. G 234 square feet
19. C 301 cubic inches
Step-by-step explanation:
It can work well to use estimation to solve both of these problems.
22. The shaded rectangular face has a height of 12 ft and a width of 20 ft. The area of a face that size is (12 ft)×(20 ft) = 240 ft². Answer choices H and J are immediately eliminated, because both are larger than that.
The cut off triangular corner will have side dimensions that are both less than 5, so it will have an area that is less than half of 5², or 25/2 = 12.5. That means the area of the shaded face will be more than ...
240 -12.5 = 227.5
Only one answer choice is in the range 228 to 240: G 234.
If you want to compute the area exactly, you can recognize that the missing triangular piece from the corner of the face has ...
a horizontal extent of 20 -16 = 4 ft
a vertical extent of 12 -9 = 3 ft
so an area given by the triangle area formula of ...
A = (1/2)bh = (1/2)(4 ft)(3 ft) = 6 ft²
Then the shaded area is ...
240 ft² - 6 ft² = 234 ft² . . . matches choice G
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19. Put the numbers from the figure into the formula and do the arithmetic.
V = (1/3)πr²h
V = (1/3)(3.14)(6 in)²(8 in) = 301.44 in³ . . . . matches choice C
