Two bodies

The rectangle with dimensions 8 cm and 4 cm is rotated 360º first around the longer side to form the first body. Then, we similarly rotate the rectangle around the shorter side b to form a second body. Determine the ratio of surfaces of the first and second bodies.

Correct result:

r =  1:2

Solution:

$$\begin{gathered} a=8\text{ cm } \\ b=4\text{ cm } \\ {r}_1=b=4=4\text{ cm } \\ {h}_1=a=8=8\text{ cm } \\ {S}_1=2\pi \cdot r_1^2+2\pi \cdot r_1\cdot h_1=2\cdot 3.1416\cdot 4^2+2\cdot 3.1416\cdot 4\cdot 8\doteq 301.5929{\text{cm}}^2 \\ {r}_2=a=8=8\text{ cm } \\ {h}_2=b=4=4\text{ cm } \\ {S}_2=2\pi \cdot r_2^2+2\pi \cdot r_2\cdot h_2=2\cdot 3.1416\cdot 8^2+2\cdot 3.1416\cdot 8\cdot 4\doteq 603.1858{\text{cm}}^2 \\ r=b:a \\ r=S_1\mathrm{/}{S}_2=301.5929\mathrm{/}603.1858={\displaystyle \frac{1}{2}}=0.5=1:2 \end{gathered}$$

Try another example

Showing 0 comments:

Next similar math problems:

• Rectangles - sides
  One side of the rectangle is 10 cm longer than second. Shortens longer side by 6 cm and extend shorter by 14 cm increases the area of the rectangle by 130 cm². What are the dimensions of the original rectangle?
• Rotary bodies
  The rotating cone and the rotary cylinder have the same volume 180 cm³ and the same height v = 15 cm. Which of these two bodies has a larger surface area?
• Rectangle - sides
  What is the perimeter of a rectangle with area 266 cm² if length of the shorter side is 5 cm shorter than the length of the longer side?
• Equilateral cylinder
  Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 199 cm³ . Calculate the surface area of the cylinder.
• Prism bases
  Volume perpendicular quadrilateral prism is 360 cm³. The edges of the base and height of the prism are in the ratio 5:4:2 Determine the area of the base and walls of the prism.
• Surface of cubes
  Peter molded a cuboid 2 cm, 4cm, 9cm of plasticine. Then the plasticine split into two parts in a ratio 1:8. From each piece made a cube. In what ratio are the surfaces of these cubes?
• Quadrangular pyramid
  Calculate the surface area and volume of a regular quadrangular pyramid: sides of bases (bottom, top): a1 = 18 cm, a2 = 6cm angle α = 60 ° (Angle α is the angle between the sidewall and the base plane.) S =? , V =?
• Base of prism
  The base of the perpendicular prism is a rectangular triangle whose legs length are at a 3: 4 ratio. The height of the prism is 2cm smaller than the larger base leg. Determine the volume of the prism if its surface is 468 cm².
• Surface of the cylinder
  Calculate the surface of the cylinder for which the shell area is Spl = 20 cm² and the height v = 3.5 cm
• Similarity
  Rectangle ABCD has dimensions of 7 cm and 6 cm. Rectangle PQRS has dimensions 14 cm and 12 cm. Determine coefficient of the similarity k of the rectangles, if they aren't similar enter zero as the coefficient of similarity.
• Surface area of cylinder
  Determine the lateral surface of the rotary cylinder which is circumscribed cube with edge length 5 cm.
• Cuboid - volume and areas
  The cuboid has a volume of 250 cm³, a surface of 250 cm² and one side 5 cm long. How do I calculate the remaining sides?
• Cuboid - ratio
  Find the volume of a block whose dimensions are in the ratio 2: 3: 4 and the surface is 117 dm².
• Four prisms
  Question No. 1: The prism has the dimensions a = 2.5 cm, b = 100 mm, c = 12 cm. What is its volume? a) 3000 cm² b) 300 cm² c) 3000 cm³ d) 300 cm³ Question No.2: The base of the prism is a rhombus with a side length of 30 cm and a height of 27 cm. The heig
• Height as diameter of base
  The rotary cylinder has a height equal to the base diameter and the surface of 471 cm². Calculate the volume of a cylinder.
• Rectangle
  The length of the rectangle are in the ratio 5:12 and the circumference is 238 cm. Calculate the length of the diagonal and area of rectangle.
• Shell area cy
  The cylinder has a shell content of 300 cm square, while the height of the cylinder is 12 cm. Calculate the volume of this cylinder.