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.
a) around its base
b) around its axis.
Correct answer:
You need to know the following knowledge to solve this word math problem:
- algebra
- expression of a variable from the formula
- arithmetic
- square (second power, quadratic)
- planimetrics
- area of a shape
- basic functions
- functions
- integral
Units of physical quantities:
Grade of the word problem:
We encourage you to watch this tutorial video on this math problem: video1
Related math problems and questions:
- Prism
Calculate the surface area and volume of a prism with a body height h = 10 cm, and its base has the shape of a rhomboid with sides a = 5.8 cm, b = 3 cm, and the distance of its two longer sides is w = 2.4 cm. - Cylinder-shaped 4411
A cylinder-shaped hole with a diameter of 12 cm is drilled into a block of height 50 cm with a square base with an edge length of 20 cm. The axis of this opening passes through the center of the base of the cuboid. Calculate the volume and surface area of - The quadrilateral pyramid
The quadrilateral pyramid has a rectangular base of 24 cm x 3.2dm and a body height of 0.4m. Calculate its volume and surface area. - Quadrangular pyramid
Given is a regular quadrangular pyramid with a square base. The body height is 30 cm, and volume V = 1000 cm³. Calculate its side and its surface area.
- Centimeters 6604
A four-sided prism has a volume of 648 cubic centimeters. The trapezoid that is its base has the dimensions a is equal to 10 centimeters, c is equal to eight centimeters, and height v is equal to 6 centimeters. Calculate the height of the prism. - Equilateral 81142
The rotating body was created by rotating an equilateral triangle with a side length of a=2 cm around one of its sides. Calculate the volume of this rotating body. - Right-angled trapezoid
A right-angled trapezoid with the measure of the acute angle of 50° is given. The lengths of its bases are 4 and 6 units. The volume of the solid obtained by rotation of the given trapezoid about the longer base is: - Prism - eq triangle
Calculate the volume and surface of the prism with the base of an equilateral triangle with side a = 4cm, and the body height is 6cm. - The height of prism
A right triangle forms the base of the vertical prism with perpendiculars 30 cm and 40 cm long. This prism has the same volume as a cube with an edge length of 3 dm. Find its height in cm.
- Hemisphere 70054
Find the volume of the spherical layer that results from a hemisphere with a radius of 5 cm by cutting a paragraph whose height is 1.5 cm. - Cylindrical 83193
How much concrete is needed to pour 8 concrete columns with a square base: a = 38 cm, the height of the columns being 6.2 m? Each column has a cylindrical cavity with a diameter of 15 cm. - Quadrilateral 15023
The regular quadrilateral pyramid has a base circumference of 44 cm and a body height of 3.2 cm. Calculate its volume and surface. - Quadrilateral 8219
Calculate the body height in a regular quadrilateral pyramid with a volume V = 163.3 cm3, whose base edge has a size a = 0.7dm. - Quadrilateral pyramid
Calculate the volume of a quadrilateral pyramid, the base of which has the shape of a rectangle with dimensions a = 6cm, b = 4cm, and height v = 11cm
- Calculate
Calculate the cone's surface and volume from the rotation of the right triangle ABC with the squares 6 cm and 9 cm long around the shorter squeegee. - Conical area
A right-angled triangle has sides a=12 and b=19 at the right angle. The hypotenuse is c. If the triangle rotates on the c side as an axis, find the volume and surface area of the conical area created by this rotation. - Tetrahedral prism
Calculate the surface and volume of a tetrahedral prism, which has a rhomboid-shaped base, and its dimensions are a = 12 cm, b = 7 cm, ha = 6 cm, and prism height h = 10 cm.