As shown in the figure, in the square ABCD with side length of 5 + 2, draw a sector with a as the center, draw a circle with o as the center, m, N, K as the tangent points, take the sector as the side of the cone, and take the circle O as the bottom of the cone to form a cone, and calculate the total area and volume of the cone

As shown in the figure, in the square ABCD with side length of 5 + 2, draw a sector with a as the center, draw a circle with o as the center, m, N, K as the tangent points, take the sector as the side of the cone, and take the circle O as the bottom of the cone to form a cone, and calculate the total area and volume of the cone

Let the generatrix length of a cone be l, the radius of its bottom be r, and the height be H. from the known conditions & nbsp; L + R + 2R = (5 + 2) 22 π r = 14 × 2 π L, r = 2, l = 42, H = l2-r2 = 30, s = π RL + π R2 = 10 π, v = 13 π r2h = 2303 π

As shown in the figure, it is a 3 × 3 square ABCD. Find the sum of ∠ 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9

∵ through observing the figure, it is found that the square ABCD is symmetrical with respect to the straight line where the diagonal BD is located, ∵ 1 + ∵ 9 = 90 °, 2 + ∵ 6 = 90 °, 3 = ∵ 5 = ∵ 7 = 45 °, 4 + ∵ 8 = 90 °, 1 + ∵ 2 + ∵ 3 + ∵ 4 + ∵ 5 + ∵ 6 + ∵ 7 + ∵ 8 + ∵ 9 = 90 °× 3 + 45 °× 3 = 405

Make a straight line L through the vertex a of cube abcd-a1b1c1d1 so that the angles formed by L and edges AB, ad and Aa1 are equal. How many such lines l can be made,
1. Make a straight line L through the vertex a of cube abcd-a1b1c1d1, so that the angles formed by L and edges AB, ad and Aa1 are equal. There are four such lines L,
2. It is known that the side edges and the bottom sides of the triangular prism abc-a1b1c1 are equal, and the projection of A1 on the bottom ABC is the midpoint of BC, then the cosine value of the angle formed by the out of plane straight line A1B and CC1 is () please explain the reason

(1) The straight line where AC1 is located is one of them. You draw the straight line where AB, ad and Aa1 are located. The three planes determined by the three straight lines divide the space into eight areas. The straight line where AC1 is located runs through two of them. Similarly, the other three can be made, so there are four in the eight areas. (2) because of CC1 / / BB1, so ∠ a1bb

How many lines are there that pass through any two vertices of the cube abcd-a'b'c'd ', which are different from ab' and whose angle is Pie / 3?
A. 2 B.3 C.4 d.5

60 degrees
4
B ` C, AC ', (a ` d, a ` C') in brackets because of parallelism