*see attachment for diagram
Answer:
Volume of new backpack = 1,299.84 in.³
Step-by-step explanation:
Volume of the new back pack = volume of the front pocket + volume of the main section of the backpack
✔️Volume of the front pocket = volume of rectangular prism = L*W*H
L = 8 in.
W = 4 in.
H = 2 in.
Volume of the front pocket = 8*4*2 = 64 in.³
✔️Volume of the main section of the back pack = volume of the rectangular prism + volume of the half cylinder
= L*W*H + ½(πr²h)
L = 12 in.
W = 10 in.
H = 7 in.
r = 6 in.
h = 7 in.
Plug in the values into the equation
Volume of the main section of the backpack = 12*10*7 + ½(π*6²*7)
= 840 + ½(791.68)
= 1,235.84 in.³
✅Total volume of the new backpack = 64 + 1,235.84 = 1,299.84 in.³
Answer:
368 sq. units.
Step-by-step explanation:
We have a square of side lengths 20 units and we cut four congruent isosceles right triangles from the corners of the square.
Now, the four isosceles right triangles have one leg equal to 4 units.
Therefore, the area of four triangles = sq. units.
Now, we have the area of the given square is (20 × 20) = 400 sq. units.
Therefore, the area of the remaining octagon will be (400 - 32) = 368 sq. units. (Answer)