1. A sphere with diameter 1 unit is enclosed in a cube of side 1 unit each. Find the unoccupied volume remaining inside the cube.
ⓐ ¼
ⓑ 2π
ⓒ π/6-1
ⓓ 1-π/4
ⓔ 1-π/6
2. The function y=3x2 is shifted 2 units towards the positive x-axis (right) and 3 units towards the positive y-axis (up). Find the resulting function.
A. y=3x2+5
B. y=3x2
C. y=3(x+2)2+3
D. y=3(x-2)2-3
E. y=3(x-2)2+3
ⓐ A
ⓑ B
ⓒ C
ⓓ D
ⓔ E
3. Find the shaded area when two squares with side ‘a’ intersect as shown in the figure below.
A. 1/8 a2
B. 1/4 a2
C. a2
D. 1/3 a2
E. 2/5 a2
ⓐ A
ⓑ B
ⓒ C
ⓓ D
ⓔ E