SKH121 wrote:
In the rectangular solid depicted above (please look at attached figure), AB = 6, BC = 8, CD = 5, and AE > EB > 2. Which of the following could be possible
values for the volume of the shaded area? Answer = D
a) 60
b) 70
c) 150
d) 170
e) 180
f) 240
Please if anyone can solve this question.
Explanation::Volume of the rectangular solid = 6 × 8 × 5 = 240.
Now the length of 2 < BE < 3 < AE < 4 because if AE is 4 then EB = 2 that violates the condition AE > EB > 2
Now we need the volume of the triangular space (Not Shaded) and there is a need to take 2 condition i.e when AE =3 and AE = 4
Volume of the triangle = Area * Height
When AE = 3 then the area of the \(\triangle\) = 12 , Volume = 12 * 5 = 60
When AE = 4 then the area of the \(\triangle\) = 16 , Volume = 16 * 5 = 80
Hence The shaded area’s volume falls between 240 – 80 = 160 and 240 – 60 = 180 i.e. Option D 170