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1. A cuboid is 8 cm long, 5 cm wide and 2 cm high. What are its surface area and volume? 2. The total edge length of a cube is 48 decimeters. What are its surface area and volume 3. A cuboid is 4 meters long, 3 meters wide and 1 meter high. What are its volume and surface area 4. The volume of a cylinder is 18 cubic decimeters, the height is 0.9 decimeters, how many square decimeters is the bottom area? 5. The bottom area of a cone-shaped sand pile is 1.5 square meters, the height is 0.4 meters, and each cubic meter of sand weighs about 1.8 tons. How many tons of sand are there in total
1) Surface area: (8 * 5 + 8 * 2 + 5 * 2) = 132 square centimeters, volume: 8 * 5 * 2 = 80 cubic centimeters. 2) 48 / 12 = 4 decimeters, surface area: 4 * 4 * 6 = 96 square centimeters, volume: 4 * 4 * 4 = 64 cubic centimeters. 3) surface area: (4 * 3 + 4 * 1 + 3 * 1) * 2 = 38 square meters, volume: 4 * 3 * 1 = 12 cubic meters
If the areas of the three common vertex surfaces of a cuboid are 3, 5 and 15 respectively, its volume is______ ．
Let the lengths of the three edges of a cuboid passing through the same vertex be a, B, C, ∵ the areas of the three surfaces starting from a vertex of the cuboid be 3, 5, 15, ∵ a · B = 3, a · C = 5, B · C = 15 ∵ a · B · C = 15, that is, the cuboid volume is 15, so the answer is: 15
If the area of three sides of a rectangle passing through a vertex is 25cm10cm10cm respectively, the volume of the rectangle is
5 × 5 = 25, 2 × 5 = 10, 2 × 5 = 10, it can be seen that the three sides of the cuboid are 5, 2 and 2 (CM), and the volume is 5 × 2 × 2 = 20 (cm3)
If the areas of the three faces at the same vertex of a cuboid are 3, 12 and 25 respectively, then its volume is____
ab=3
bc=12
ac=25
ab*bc*ac=(abc)^2=900
abc=30
Volume = ABC = 30
If the area of the three faces of the cuboid passing through one vertex is 25, 10 and 10, the volume is
Let ABC be three sided
From the theme
ab = 25
bc = 10
ac = 10
（abc）^2 = 2500
abc = 50
The volume is 50
It is known that the areas of the three faces intersecting at a vertex in a cuboid are 3, 4 and 6, respectively?
Volume: 3 × 4 × 6 = 72
A2 + B2 = 4, C2 + D2 = 10, AC + BD = 2, find the value of ad BC
2 is the square (the last one is not)
(a2+b2)(c2+d2)=4*10;
=a2c2+a2d2+b2c2+b2d2=40
a2c2+a2d2=40-b2c2-b2d2
Take 40-b2c2-b2d2 into the following equation
AC + BD = 2, both sides are equal in square;
a2c2+2abcd+b2d2=4
40-b2c2-b2d2+2abcd=4
b2c2+b2d2-2abcd=36
（ad-bc)2=36
Ad BC = 6 or ad BC = - 6
Given a 2-B 2-5 = 0, C 2-D 2-2 = 0, find the value of (AC + BD) 2 - (AD BC) 2
If there is a mistake in the estimation, you can change a minus sign into a plus sign in the middle
In the triangle ABC, the angle ACB is 90 degrees, D is the midpoint of BC, De is vertical to BC, CE is parallel to ad, AC is equal to 2, CE is equal to 4, and the perimeter of the quadrilateral abce
Analysis: first prove that quadrilateral aced is a parallelogram, and get de = AC = 2. By Pythagorean theorem and the definition of the middle line, we can find the length of AB and EB, so as to find the perimeter of quadrilateral aceb. ∵ ACB = 90 °, de ⊥ BC, ∵ AC ∥ De. and ∵ CE ∥ ad, ∵ quadrilateral aced is a parallelogram. ∵ de = AC = 2
In triangle ABC, points D and E are on AB respectively. Let CD and be intersect at O, angle a = 60 degrees, angle DCB = angle EBC = 1 / 2 angle A. please write
An angle equal to angle a in a graph, and guess which quadrilateral in the graph is a pair of equilateral quadrilateral
Angle COE = angle a
A quadrilateral bced is an equilateral quadrilateral (truncate EF = do and prove that △ COF and △ BOD are congruent)
Beijing senior high school entrance examination questions
RELATED INFORMATIONS
- 1. In △ ABC, points D and E are AB and AC respectively. Let CD and be intersect at point O. if ∠ a = 60 °, DCB, EBC = half a, find an angle equal to a
- 2. In △ ABC, B & # 178; = A & # 178; + C & # 178; - AC, then the value of B is
- 3. It is known that: in △ ABC, the edges of angles a, B and C are a, B and C respectively, and a & # 178; + C & # 178; - B & # 178; = # 189; AC (1) Find the value of cos2b (2) If B = 2, find the maximum area of △ ABC
- 4. In △ ABC, 2b = a + C, B & # 178; = AC, then △ ABC must be () A. Acute triangle B, obtuse triangle C, isosceles triangle D, equilateral triangle The scope is the five required exercises of sine theorem and cosine theorem in mathematics,
- 5. Let a, B, C opposite the three interior angles of △ ABC, if its area s = C ^ 2 - (a-b) ^ 2, then Tan (C / 2) =?
- 6. In the triangle ABC, if a is known to be an acute angle and B = 3asinb, then Tana=
- 7. In the triangle ABC, we know that 2sinbxcosc = Sina, a = 120 degrees, a = 1, and find the area of B and triangle ABC
- 8. In △ ABC, note that a, B and C are opposite sides of a, B and C respectively, and S is the area of triangle, and prove that C ^ 2-A ^ 2-B ^ 2 + 4AB ≥ 4 √ 3S This is the 19th question of the test paper. It's not very difficult, but I haven't thought about it for a long time. Please help me solve it~ PS: because the characters are not standard, I'll use words to explain it again. Verification: the square of C minus the square of a minus the square of B plus 4AB is greater than or equal to 4 times the root sign 3 times s~
- 9. It is known that a and B belong to (0, positive infinity), and 2C > A + B
- 10. If A2 + B2 + c2-ab-3b-2c + 4 = 0, then the value of a + B + C is______ ．
- 11. The length, width and height of a cuboid are respectively ABC decimeters. If the height increases by 2 decimeters, the volume increases (); the surface area of cubic centimeter increases () square decimeters
- 12. Add three numbers after 865 to form a six digit number, so that it can be divided by 3, 4 and 5 respectively, and make the value as small as possible, then the six digit number is______ ．
- 13. If there is a 1994 digit a which can be divided by 9, the sum of its digits is B, and the sum of its digits is C, then C =?
- 14. A three digit number is represented by ABC. It is known that it can be divided by 2, 3 and 5 at the same time, and a + C = 8. What is the three digit number?
- 15. In triangle ABC, a, B and C are the opposite sides of angles a, B and C respectively. If (a + B + C) (B + C minus a) is equal to 3bC, the value of angle a can be obtained
- 16. In the triangle ABC, the angle c = 90 ° and CE is the middle line of the triangle ABC. If AC = 4 and BC = 3, what is the area of the triangle AEC?
- 17. Let the inner angles a, B and C of △ ABC be opposite to a, B and C respectively. We know that a = 4, B = 5 and C = 61. (I) find the size of angle c; (II) find the area of △ ABC
- 18. The new operation X & y = ax + by + C, a, B, C of the definition of rational number XY are the values of 2-7 when 1 & 2 = 9-3 & 3 = 60 & 1 = 2 is known
- 19. In △ ABC, ∠ C = 90 °, ab = 41, the perimeter of △ ABC is 90, try to find the area of △ ABC,
- 20. The trilateral lengths a, B and C of △ ABC satisfy a + B = 8, ab = 4 and C2 = 56. Try to judge the shape of △ ABC and explain the reason