The sum of the two bottom surfaces of a cylinder is equal to the side area

The sum of the two bottom surfaces of a cylinder is equal to the side area

Let the bottom radius of the cylinder be r, 2 π R2 = 2 π R × 8 & nbsp; & nbsp; r = 8, and the volume of the cylinder be 3.14 × 82 × 8 = 200.96 × 8, = 1607.68 (cubic centimeter). A: the volume of the cylinder is 1607.68 cubic centimeter

When the height of a cylinder increases by 1 cm, the surface area of the cylinder increases by 31.4 square cm. It is known that the original height of the cylinder is 10 cm, and the original volume is 10 cm______ Cubic centimeter

31.4 ﹣ 1 ﹣ 3.14 ﹣ 2 = 5 (CM), 3.14 × 52 × 10, = 3.14 × 25 × 10, = 785 (cm3), answer: the original volume is 785 cm3; so the answer is: 785

The diameter of the bottom surface of a cylinder is 10 cm. If the height increases by 2 cm, how many square centimeters will the side area increase?

3.14×10×2
=31.4×2
=62.8（㎝²）
Answer: side area increases 62.8 square centimeter

If the bottom area of the cylinder remains unchanged, the height increases by 3 cm and the surface increases by 1130.4,
Calculate the surface area

Bottom perimeter: 1130.4 △ 3 = 376.8 cm
Radius: 376.8 △ 3.14 △ 2 = 60cm
Original surface area: 3.14 × 60 & # 178; × 3 = 33912 square cm

There is a cylinder with a bottom diameter of 12 cm. If its height increases by 2 cm, how many square centimeters does its side area increase?

RM burning glass summer,
3.14 × 12 × 2 = 75.36 (cm2)

Finding the surface area of space geometry
The side lengths of the upper and lower surfaces of a regular triangular platform are 3cm and 9cm respectively, and the body height is 3cm

The projection of the side on the bottom is a trapezoid, the length of the top and bottom is 3 and 9 respectively, the hypotenuse is 30 ° to the bottom, the height = ((9-3) / 2) × Tan 30 ° = 3 ^ 0.5, the height of the side projection trapezoid, the height of the regular triangular platform and the height of the side projection trapezoid form a right triangle, the height of the side projection trapezoid = 3 ^ 0.5, the height of the regular triangular platform = 3

It is known that the base radius of a cone is R and its height is 3R. In all its inscribed cylinders, the maximum of its total area is______ ．

Let the bottom radius of inscribed cylinder be r, the height be h, and the total area be s, then 3R − h3r = RR  H = 3r-3r 〉 s = 2 π RH + 2 π R2 = - 4 π R2 + 6 π RR = - 4 π (r2-32rr) = - 4 π (r-34r) 2 + 94 π R2 〉 when r = 34R, the maximum value of S is 94 π R2. So the answer is: 94 π R2

How to calculate the surface area and volume of space geometry?

If it's simple, you need to divide the space geometry into several simple geometry whose surface area and volume formula you know, and then the volume sum of each simple geometry is the volume of the space geometry; the sum of the common surface area of each simple geometry and the space geometry is the surface area of the space geometry

If the front view and side view of a space geometry are two squares with side length of 1, and the top view is an isosceles right triangle with right angle side length of 1, then the surface area of the geometry is equal to ()
A. 2+2B. 3+2C. 4+2D. 6

According to the three views, the geometry is a straight triangular prism with an isosceles right triangle at the bottom. The length of the right side at the bottom is 1; the height of the prism is 1. So the surface area of the triangular prism is 2S bottom + s side = 2 × 12 × 1 × 1 + 1 × (1 + 1 + 2) = 3 + 2

It is known that three planes α, β and γ intersect each other on three straight lines, that is, α ∩ β = C, β ∩ γ = a, γ ∩ α = B. If a and B are not parallel, it is proved that a, B and C must pass through the same point

If C and B intersect at a point, let C ∩ B = P. from P ∈ C, and C ⊂ β, there is p ∈ β; from P ∈ B, B ⊂ γ, there is p ∈ γ; ∩ P ∈ β ∩ γ = a; therefore, a, B, C intersect at a point (i.e. P point)