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The right figure ABCD is a right angled trapezoid. Take CD as the axis and rotate the trapezoid around this axis to get a rotating body. How many cubic centimeters is its volume?
If you rotate with the waist as the right angle side, it is the difference between the volume of the big rhomboid and that of the small rhomboid. If you rotate with the bottom as the right angle side, it is the difference between the volume of the cylinder and that of the middle small rhomboid
As shown in the figure, ab ∥ DC, ab = 7cm, BC = CD = 4cm in right angle trapezoid ABCD. Take the straight line where AB is as the axis to rotate for one circle to get a geometry and calculate its full area
In ∵ RT △ AOD, Ao = 7-4 = 3cm, OD = 4cm, ∵ ad = 42 + 32 = 5cm, ∵ the surface area of the obtained geometry is π × 4 × 5 + π × 4 × 2 × 4 + π × 4 × 4 = 68 π cm2. Therefore, its total area is 68 π cm2
In known trapezoidal ABCD, ab ∥ CD, ∠ B = Π / 2, DC = 2Ab = 2BC = 2, the surface area of the geometry obtained by rotating a circle around the straight line ad is ()
A 4√2∏ B 7/2√2∏ C 3√2∏ D 2√2∏
A.4√2π
The geometry obtained after rotation is: ab forms the concave cone side, BC forms the cone side, CD forms the large cone side
The area of the concave cone and the side of the frustum is just equal to that of the large cone
Large cone side area S1 = 2 √ 2 π · 2 / 2 = 2 √ 2 π
S=2S1=4√2π
As shown in the figure, in the right angle trapezoid ABCD, AB is parallel to CD, ab ⊥ BC, ∠ a = 60 °, BC = 2 root sign 3. DC = 3, rotate one circle with the straight line where AB is located as the axis, and calculate the
The volume and surface area of the geometry formed by rotating a circle with ab as the axis? The geometry formed by rotating a circle with ab as the axis is a combination of cylinder and cone, with bottom radius length = BC = 2 root sign 3; make de perpendicular to AB, perpendicular foot e, de = BC = 2 root sign 3; EB = CD = 3; ∠ ade = 90 ° - a = 30 °
It is known that the side ab of a cube ABCD has a length of 2. If a geometry is formed by taking a straight line of its side AB as the axis of rotation, then the volume of the geometry is
Process thank you
The geometry is a cylinder with 2 times radius, 2 times root sign and 2 times height
Volume = (2 times the square of radical 2) × π × 2
＝16π
As shown in the figure, in the known rectangle ABCD, ab = 2, BC = 4, rotate the rectangle around one side, and the area of the enclosed geometry is
When the enclosed geometry is a cylinder with the side of the rotation axis as the height and the other side as the radius, the surface area of x0d geometry is: 2 * π * AB ^ 2 + 2 π * AB * BC = 24 π the surface area of x0d geometry is: 2 * π * BC ^ 2 + 2 π * BC * AB = 48 π
As shown in the figure, ABCD is a rectangle, ab = 4, ad = 6. Is the volume of two cylinders obtained by rotating around AB and BC the same?
Hope everyone to reply soon
When AB is high, the volume is large
As shown in the figure, in the pyramid p-abcd, the side pad ⊥ bottom ABCD, PA = PD = 2, and the bottom ABCD is a right angle trapezoid, where BC is parallel to ad, AB is vertical to ad, ad = 2Ab = 2BC = 2 root 2
1》 Finding the angle between PC and pad
2》 Find the size of dihedral angle a-pb-c
Take the midpoint e of Da, link CE and PE, because PA = PD = 2, then PE ⊥ ad, then CE = root 2, PEC ⊥ bottom ABCD, PC = 2, because AB is vertical ad, ad = 2Ab = 2BC = 2, root 2, then PEC ⊥ side APD is calculated, PE = root 2, CE = root 2, then the angle between PC and pad is 45 degrees, make AF ⊥ Pb intersection from a to F, connect CF
As shown in the figure, in ladder ABCD, ad ‖ BC, ab = DC, P is a point outside the ladder ABCD, PA and PD intersect BC at points E and f respectively, and PA = PD. (1) write three pairs of triangles that you think are congruent in the graph (no auxiliary lines are added); (2) select any pair of congruent triangles that you write in (1) to prove
(1) (2) the following is the reference answer of △ ABP ≌ DCP; (2) the following is the reference answer of 8780 ≌ DCP; ② \ \≌ DCF; ③ \\\\\ \\\\\\\indcp ∵ PA = PD ∠ BAP = - ∠CDPAB＝DC∴△ABP≌△DCP．
As shown in the figure, in the pyramid p-abcd, PA ⊥ plane ABCD, bottom ABCD is right angle trapezoid, ab ⊥ ad, CD ⊥ ad, CD = 2Ab, e is the midpoint (1) verification: plane PDC ⊥ plane pad (2) verification: be ∥ plane pad
1. PA ⊥ planar ABCD, PA ⊥ cdcd ⊥ ad CD ⊥ planar padcd is in planar PDC, so planar PDC ⊥ planar PaD2. E is the midpoint of PC, take PD midpoint m, connect em, aMEM / / = 1 / 2cdab / / = 1 / 2cdem / / = AB quadrilateral, EMAb is parallelogram, so be / / AMBE is outside planar pad, am is in planar pad, so be
RELATED INFORMATIONS
- 1. 17. As shown in the figure, in the pyramid p-abcd, the bottom surface is a right angled trapezoid, ad ‖ BC, ∠ bad = 90 °, PA ⊥ bottom surface ABCD, and PA = ad = AB = 2BC, m, n respectively If the first question is proved, ask the second question. Please don't use vectors
- 2. In a park, three channels with the same width are built on a rectangular ground ABCD with a length of 40 meters and a width of 26 meters (as shown in the figure), two of which are parallel to AB and the other is vertical to ab. these three channels divide the ABCD into small rectangular blocks with an area of 144 square meters, and plant six colors of flowers and plants respectively to calculate the width of the channel
- 3. As shown in the figure, there is a quadrilateral piece of paper ABCD, ab ‖ CD, ad ‖ BC, ∠ a = 60 degrees. Fold the paper along the crease Mn and PQ respectively, so that point a coincides with point E on the edge of AB, point C coincides with point F on the edge of CD, eg bisection ∠ MEB intersects CD at g, FH bisection ∠ PFD intersects AB at h. try to explain: (1) eg ‖ FH; (2) me ‖ PF
- 4. As shown in the figure, in square ABCD, if DP intersects the extension lines of AC, AB and CB at m, N, P, Mn = 1, NP = 3, then DM=______ ．
- 5. In rectangular trapezoid ABCD, ad is parallel to BC, ∠ a = 90 degrees, ab = ad = 1 / 2BC, and m and N are the midpoint of AD and DC respectively, connecting BM, Mn and BN. Excuse me: triangle What is the triangle of BmN
- 6. As shown in the figure, the parallelogram ABCD, e is the midpoint of AD, AC and be intersect at the point F, s △ EFC = 1, then s parallelogram ABCD=
- 7. If the perimeter of the diamond is 8cm and the height is 1cm, the angle of the diamond is smaller______ ．
- 8. Given that the length of a diagonal line of a diamond is 4cm and the perimeter is 16cm, what are the degrees of the four inner angles of the diamond?
- 9. As shown in the figure, the quadrilateral ABCD is a square, AB is an equilateral triangle with an edge to the square, Abe, CE and DB intersect at point F, then ∠ AFD=______ Degree
- 10. As shown in the figure, in ladder ABCD, ab ‖ DC and E are the midpoint of BC, and the extension lines of AE and DC intersect at point F to connect AC and BF. What quadrilateral is abfc? Please give reasons
- 11. The area of quadrilateral ABCD is 30, e and F are the three equal parts of AB, m and N are the three equal parts of DC. The area of efnm is calculated
- 12. The side length of square ABCD is 4, M is the middle point of AD, the moving point e moves on the line AB, connects EM and extends the intersection line CD and F, and makes the intersection line of EF through M BC and G, connect eg and FG, prove that let AE = x, the area of △ EGF = y, find the analytic formula and value range of Y and X. can △ GEF be an equilateral triangle during the movement of 2 points e? Please explain the reason
- 13. English translation English
- 14. Red pigment + yellow pigment red pigment + blue pigment yellow pigment + blue pigment
- 15. If the front view and top view of a triangular prism with equal edge lengths are square and regular triangle respectively, then the left view is () A. Rectangle B. square C. diamond D. regular triangle
- 16. The side length of the bottom of the hexagonal prism is equal to 1, and the side length is 2. After the side of the prism is expanded along a side edge, the area of the side expansion is calculated
- 17. The square ABCD is rotated clockwise around point a to obtain the quantitative relationship of square aefg, the intersection of edge FG and BC, aefc, the intersection of edge FG and BC, h, Hg and Hb
- 18. The quadrilateral ABCD and the quadrilateral aefg are both rhombic. The point E is on the ad side and the point G is on the extension line of the Ba side As shown in Figure 1, BD and CE are their diagonals. The extension line of Ge intersects BD at point Q and DC at point M. verify: GM ⊥ BD
- 19. As shown in the figure, in ▱ ABCD, e and F are two points on the diagonal BD, and be = DF
- 20. A piece of rectangular paper with a length of 5cm and a width of 4cm is rotated around its length and width respectively to form two cylinders. Which cylinder has the largest volume should be estimated first and then calculated