tricky geometry

Fab wrote:Please be clear with the explanations.

THANKS!

Please post them seperately with the source. This way, people can solve one question at a time, and search it in the future. Thanks.

Q1
consider statement 1
if AB= 3 and BC =2
area of smaller = pi.Ab^2
and area of larger = pi.(AB + BC)^2)
so we can subtract and get the desired area.
Statement b does not help because we can't calculate area of smaller with this.

I agree with you, however the OA for question 1 is D (apparently).
I don't know what's the source, a fried of mine passed me the exams.

THANKS.

Q30:
Answer B? B. (sqrt2)/4

Area of BCE = Area of BEO - Area of BOC

(1+(sqrt2)/2)*((sqrt2)/2)*1/2 - (sqrt2)/2)*(sqrt2)/2)*1/2 = (sqrt2)/4

1. D

We need the difference in area, i.e. the radii of both circles
First statement: Gives us the radii of both circles: AB (smaller circle), and AB+BC (larger circle) Sufficient
Second statement: CD+DE = radius of larger circle; 2 (CD+DE)-DE = AD = diameter of smaller circle. So we have the radii of both circles again. Sufficient

2. Max height of the semicircular tunnel = 20/2 = 10ft
Clearance required = 1/2 ft
Therefore, max height allowed = 10-(1/2) = 9(1/2) ft

3. See the previous post w/ diagram

for the second question:

I got the max height as 7,5.

i think, the max height without clearance can't be 10, because the width of the vehicle is 12, the width remains the same for the top part of the vehicle as well. well, here we have a rectangilar inscribed in a semicircle. since the radius of the semicircle is 10, and the width if the rectangle 12, its length will be sqrt(10^2-6^2)=8
8-1/2=7 1/2

am i missing smth?

Second statement: CD+DE = radius of larger circle; 2 (CD+DE)-DE = AD = diameter of smaller circle. So we have the radii of both circles again. Sufficient

Are you sure??

Isn't it CD + DE - DE = CD?

Fab wrote:

Second statement: CD+DE = radius of larger circle; 2 (CD+DE)-DE = AD = diameter of smaller circle. So we have the radii of both circles again. Sufficient

Are you sure??

Isn't it CD + DE - DE = CD?

See carefully,
(CD+DE) = radius of larger circle
2*(CD+DE) = diameter of the larger circle
2*(CD+DE)-DE= diameter of smaller circle...enough info to get the area of both circles.

Muzali-- Excellent approach to solve these problems...Thanks!!