The parabolic segment

The parabolic segment has a base a = 4 cm and a height v = 6 cm. Calculate the volume of the body that results from the rotation of this segment

a) around its base
b) around its axis.

Correct answer:

V1 =  51.2 cm3
V2 =  50.2655 cm3

Step-by-step explanation:

a=4 cm v=6 cm f(x)=qx2 f(a/2)=q(a/2)2=v 6=q 22  q=6/22=32=1.5  V1=815 v a2=815 6 42=2565 cm3=51.2 cm3
f(x)=v64x2 f(x)=664x2  x0=a/2=4/2=2 x1=a/2=4/2=2  V2=π x0x1f(x)dx V2=π x0x1(64x2v)dx V2=π [64 x3/3vx]x0x1  F(x)=6x64 x3/3 F1=6 x164 x13/3=6 264 23/3=8 F0=6 x064 x03/3=6 (2)64 (2)3/3=8  V2=π (F1F0)=3.1416 (8(8))=50.2655 cm3

Did you find an error or inaccuracy? Feel free to write us. Thank you!


We encourage you to watch this tutorial video on this math problem: video1

Related math problems and questions:

  • Triangular prism
    prism3 The triangular prism has a base in the shape of a right triangle, the legs of which is 9 cm and 40 cm long. The height of the prism is 20 cm. What is its volume cm3? And the surface cm2?
  • Uboid volume
    cuboid Calculate the cuboid volume if the walls are 30cm², 35cm², 42cm²
  • Cuboid and eq2
    kvader11 Calculate the volume of cuboid with square base and height 6 cm if the surface area is 48 cm2.
  • Spherical segment
    SphericalSegment Calculate the volume of a spherical segment 18 cm high. The diameter of the lower base is 80 cm, the upper base 60 cm.
  • Truncated pyramid
    truncated_pyramid The truncated regular quadrilateral pyramid has a volume of 74 cm3, a height v = 6 cm, and an area of the lower base 15 cm2 greater than the upper base's content. Calculate the area of the upper base.
  • Diameter = height
    valec The cylinder's surface, the height of which is equal to the diameter of the base, is 4239 cm square. Calculate the cylinder volume.
  • Square
    percent Suppose the square's sides' length decreases by a 25% decrease in the content area of 28 cm2. Determine the side length of the original square.
  • Triangular pyramid
    triangularPyramid A regular tetrahedron is a triangular pyramid whose base and walls are identical equilateral triangles. Calculate the height of this body if the edge length is a = 8 cm
  • Quadrangular pyramid
    jehlan_4b_obdelnik Given is a regular quadrangular pyramid with a square base. The body height is 30 cm and volume V = 1000 cm³. Calculate its side a and its surface area.
  • Rotation
    cone The right triangle with legs 11 cm and 18 cm rotate around the longer leg. Calculate the volume and surface area of the formed cone.
  • Pyramid cut
    ihlan_rez We cut the regular square pyramid with a parallel plane to the two parts (see figure). The volume of the smaller pyramid is 20% of the volume of the original one. The bottom of the base of the smaller pyramid has a content of 10 cm2. Find the area of the
  • Triangular prism
    hranol3b The base of the perpendicular triangular prism is a rectangular triangle with a hypotenuse of 10 cm and one leg of 8 cm. The prism height is 75% of the perimeter of the base. Calculate the volume and surface of the prism.
  • Equilateral cylinder
    3d Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 199 cm3 . Calculate the surface area of the cylinder.
  • Rhombus base
    paral_prism Calculate the volume and surface area of prisms whose base is a rhombus with diagonals u1 = 12 cm and u2 = 15 cm. Prism height is twice the base edge length.
  • Regular square prism
    cuboid_3colors The volume of a regular square prism is 192 cm3. The size of its base edge and the body height is 1: 3. Calculate the surface of the prism.
  • Trapezoid
    hexphitri Area of trapezoid is 135 cm2. Sides a, c and height h are in a ratio 6:4:3. How long are a,c and h? Make calculation...
  • Calculate
    kuzel3 Calculate the cone's surface and volume that results from the rotation of the right triangle ABC with the squares 6 cm and 9 cm long around the shorter squeegee.