![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
For a cube wood block with 10 cm edge length, dig a small cube with 2 cm edge length in the center of front and back, left and right, upper and lower sides respectively, and calculate the surface area of the block
10 × 10 × 6 + 2 × 2 × 4 × 6, = 600 + 96, = 696 (cm2)
For a cube with an edge length of 10 cm, a cylindrical hole with a diameter of 2 cm and a depth of 2 cm (without overlapping part) is dug out on each surface to calculate the surface area?
The calculated surface area = the surface area of cube + the area of six cylindrical surfaces = 10 * 10 * 6 + π * 2 * 2 * 6 = 600 + 75.36 = 675.36 CM & # 178;
What is the surface area of a cube with 10 cm edge length after digging out a cube with 2 cm edge length?
Where to dig the corner?
There are three cases
1. Dig in the corner. The surface area remains unchanged
2. Dig on the edge (not close to the corner), with more than two small cubes, and the surface area is 600 + 8 = 608 CM & # 178;
3. On the surface (not close to the edge), there are more than four small cubes, the surface area is 600 + 16 = 616 CM & # 178;
On a cuboid with a length of 10cm, a width of 6cm and a height of 5cm, dig out a cube with an edge length of 2cm. What is the surface area of the remaining part
It depends on how to dig
1. Digging on any corner, the surface area remains unchanged;
2. Dig on any side with a surface area of 2 * 2 * 2 = 8 (square centimeter);
The remaining surface area is (10 * 6 + 10 * 5 + 6 * 5) * 2 + 8 = 288 (square centimeter)
3. Dig in the middle of any surface and increase the surface area by 2 * 2 * 4 = 16 (square centimeter)
The remaining surface area is (10 * 6 + 10 * 5 + 6 * 5) * 2 + 16 = 296 (square centimeter)
Find the area of the plane figure enclosed by the curve y = cosx and x = 0, x = π, y = 0
This problem is transformed into definite integral
∫[0,π]cosxdx
=2∫[0,π/2]cosxdx
=2sinx[0,π/2]
=2
1, find the curve y = cosx (0
Using definite integral:
∫[0,π/2]cosxdx
=∫[0,π/2]cosxdx
=sinx[0,π/2]
=1
For ∫ [0, π / 2] π cos ^ 2xdx
=∫[0,π/2]π/2(1+cos2x)dx
=π/2(x+1/2sin2x)[0,π/2]
=π/2(π/2-0)
=π^2/4
The parameter equation (such as the supplementary question) represents the graph (multiple choice question)
The parameter equation is: x = 3 + 3cos θ
y=-3+3sinθ
The center of a is (- 3,3), the radius is 9, the center of B is (- 3,3), the radius is 3
C center is (3, - 3), radius is 9, D center is (3, - 3), radius is 3
C.
X = 3 + 3cos θ, that is, x-3 = 3cos θ,
Y = - 3 + 3sin θ, that is, y + 3 = 3sin θ
(x-3) ^ 2 + (y + 3) ^ 2 = 9. The graph represented by this equation is C
How to draw parameter equation with graphic calculator
I'm from Casio fx9750 GII,
How to solve the surface equation of revolution surface and its equation?
Let f (y, z) = 0
Rotate around the z-axis, the result is: Z does not move, rewrite y as: ± √ (X & # 178; + Y & # 178;)
That is: F (± √ (X & # 178; + Y & # 178;), z) = 0
If it revolves around other axes, it will be treated similarly
Find the specific solution to the problem of "parabola Z & # 178; = 3x rotates around the x-axis to produce a surface of revolution equation"
RELATED INFORMATIONS
- 1. A problem of rotation equation in advanced mathematics, The curve 4x ^ 2-9x ^ 2 = 36 on the oxy plane, the equation obtained by rotating around the X axis and Y axis, please write in detail,
- 2. Higher mathematics problem: how to calculate the surface area of the ball by the integral of the circumference? Sphere surface area s = 4 * Pai * r * r How to use it Circumference C = 2 * Pai * r Integral? Is it S=2∏＊∫0 R∫0 ∏/2 r* sinθ dr * dθ =4∏R2 ? (for format problem, superscript and subscript are inseparable, ∫ is the integral sign, ∫ 0 R means the product from 0 to R)
- 3. Figure area enclosed by curve and straight line The area enclosed by the curve y = x ^ 3 + 1, the straight line x + y = 3 and two coordinates
- 4. In a semicircle, draw a maximum right triangle with the center point o as the right vertex. It is known that the area of the triangle is 25 square meters. How about the area of the circle?
- 5. Through the point P (- 2, - 3), make two tangents of the circle C: (x-4) ^ 2 + (Y-2) ^ 2 = 9, the tangent points are a ` B respectively. Find the square of the circle passing through the center C and the tangent point is A.B
- 6. Q.2 analytic geometry straight line and circle, hope to answer as soon as possible, 1. It is known that a circle centered on point C (T, 2 / T) (t ∈ R, t ≠ 0) intersects with X-axis at point O and point a, and intersects with Y-axis at point O and point B, where point O is the origin of rectangular coordinate system. Let y = - 2X + 4 intersect with circle C at point m, N, and if om = on, find the equation of circle C 2. Let the image of the quadratic function f (x) = x & # 178; + 2x + B (x ∈ R) have three intersections with the two coordinate axes in the plane rectangular coordinate system xoy, and the circle passing through the three intersections is marked as C (1) I have worked out the value range of B
- 7. How to prove the symmetry theorem of double integral This theorem is very good, but I want to know the principle, which is the process of proving this theorem
- 8. Using polar coordinates to calculate double integral ∫ [D] (6-3x-2y) DXDY =? Where D: x ^ 2 + y ^ 2
- 9. The equation for the projection of line L on the plane Π: x + y + 2z-5 = 0 is obtained
- 10. What is the value of the real number a if the length of the line X-Y = 2 cut by the circle (x-a) & sup2; + Y & sup2; = 4 is the root 2
- 11. Half of the square metal block with a side length of 10 cm is placed on a plane with an area of 1 square meter. When the indication of the spring dynamometer is 10 N, the pressure is 4 times 10 cubic PA, and the density of the metal block is calculated G is 10N / kg, the answer is 5 * 10 ^ 3kg / m ^ 3
- 12. Find the maximum area and perimeter of inscribed rectangle of ellipse x 2 / a 2 + y 2 / B 2 = 1 (a > b > 0)
- 13. Given the ellipse x ^ 2 / 9 + y ^ 2 / 4 = 1, find the maximum area of its inscribed rectangle
- 14. If a straight line passing through the center of the ellipse x ^ 2 / 25 + y ^ 2 / 16 = 1 intersects the ellipse at two points a and B, and F is a focal point of the ellipse, what is the maximum area of △ ABF Such as the title Why are a and B symmetrical about o. Not quite understand
- 15. A vertex on the major axis of the ellipse x2 + 4y2 = 4 is a. take a as the right vertex to make an isosceles right triangle inscribed on the ellipse. The area of the triangle is______ ．
- 16. Given the inscribed rectangle ABCD of the ellipse x2 / A2 + Y2 / B2 = 1 (a > b > 0) (ABCD is all on the ellipse), find the maximum face of the rectangle
- 17. The inscribed rectangle of ellipse A & # 178; / X & # 178; + B & # 178; / Y & # 178; = 1 has all fixed points on the ellipse. What is the maximum area of the rectangle?
- 18. The line passing through a focal point of ellipse 2x & # 178; + Y & # 178; = 2 intersects the ellipse at two points P and Q to find the maximum area of △ poq?
- 19. It is known that the center of the ellipse C is at the origin, the focus is on the x-axis, one of its vertices is (0,1), and the eccentricity is equal to 2 / 5 of the original number 5 (1) Please write down the specific process!
- 20. The maximum inscribed rectangle problem of ellipse Make an inscribed rectangle in the ellipse of x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 to maximize the area of the rectangle My approach is: Let the vertex coordinates of the rectangle in the first quadrant be (acosx, bsinx) Then the length of the rectangle is 2acosx and the width is 2bsinx, Area = 4absinxcosx = 2absin2x Then, when x = 45 degrees, the area is the largest, then, when the area of the inscribed rectangle is the largest, don't they all become square? The length and width of the rectangle are √ 2a and √ 2B The maximum area of rectangle is s = 2p * 2q = 2Ab ", which is wrong?