1. A sphere is sliced so that the cross section does not intersect the center of the sphere.What is the shape of the cross section?squarecirclerectanglesemicircle2. What is the area of a cross section that is parallel to face ABCD ?3. What is the area of the two-dimensional cross section that is parallel to face ABC ?4. This rectangular prism is intersected by a plane that contains points B, D, H, and F.What is the perimeter of the cross section?(the first picture is for 2, the second is for 3, the third is for 4)
Accepted Solution
A:
1. The shape of cross-section is a circle. 2. The face parallel to ABCD is EFGH. Since this is a a rectangular shape,
A = L*H = 12*6 = 72 cm^2
3. The cross-section parallel to ABC is DEF with h = 12 ft, b= 5ft (where h is the height and b is the base of a right angled triangle).
Area, A = 1/2 *b*h = 1/2*5*12 =30 ft^2
4. Plane BDHF is a rectangle shape whose length is the diagonal of ABCD.
Diagonal BD = sqrt (AB^2+BD^2) = sqrt (8^2+7^2) = 10.63 cm. Perimeter, P = 2(BD+DH) = 2(10.63+6) = 33.26 cm