Answer
Verified
456.9k+ views
Hint: A set of points in the space at a distance \[r\] from a fixed point (center) is known as the sphere. It is a perfectly round object in 3-dimensional space with no edges or vertices and is a perfectly symmetrical object. It is drawn on the three-axis x-axis, y-axis, and z-axis.
The volume of a shape is generally referred to as the capacity it has, or it can hold. The volume of the sphere determines the capacity of the gaseous state that can behold in it. The volume of the sphere is directly dependent on its diameter \[V \propto d\]; the larger the diameter of the sphere, the greater is its capacity, and the smaller the diameter of the sphere, the lesser capacity it has.
Complete step by step answer:
The volume of a Sphere is given as \[V = \dfrac{4}{3}\pi {r^3}\], where \[r\] is the radius of the sphere. Radius is the total distance of the center of the sphere to its boundary. Radius is represented as \[r = \dfrac{d}{2}\], where \[d\] is the diameter of the sphere.
The diameter of the sphere is given as \[d = 8{\text{ }}mm\] hence the radius will be:
\[
r = \dfrac{d}{2} \\
= \dfrac{8}{2} = 4mm \\
\].
So the volume of the sphere will be:
\[
V = \dfrac{4}{3}\pi {r^3} \\
= \dfrac{4}{3}\pi {\left( 4 \right)^3} \\
= \dfrac{4}{3} \times 3.14 \times 4 \times 4 \times 4 \\
= \dfrac{{256 \times 3.14}}{3} \\
= 267.95{\left( {mm} \right)^3} \\
\]
Hence, the volume of the sphere is 267.95 cubic milli-meters.
Note: To find the capacity of a closed curve/body, the volume is calculated for a three-dimensional object, and the area is calculated for a two-dimensional figure. The three-dimensional sphere is obtained when a two-dimensional circle is rotated about its symmetry.
The volume of a shape is generally referred to as the capacity it has, or it can hold. The volume of the sphere determines the capacity of the gaseous state that can behold in it. The volume of the sphere is directly dependent on its diameter \[V \propto d\]; the larger the diameter of the sphere, the greater is its capacity, and the smaller the diameter of the sphere, the lesser capacity it has.
Complete step by step answer:
The volume of a Sphere is given as \[V = \dfrac{4}{3}\pi {r^3}\], where \[r\] is the radius of the sphere. Radius is the total distance of the center of the sphere to its boundary. Radius is represented as \[r = \dfrac{d}{2}\], where \[d\] is the diameter of the sphere.
The diameter of the sphere is given as \[d = 8{\text{ }}mm\] hence the radius will be:
\[
r = \dfrac{d}{2} \\
= \dfrac{8}{2} = 4mm \\
\].
So the volume of the sphere will be:
\[
V = \dfrac{4}{3}\pi {r^3} \\
= \dfrac{4}{3}\pi {\left( 4 \right)^3} \\
= \dfrac{4}{3} \times 3.14 \times 4 \times 4 \times 4 \\
= \dfrac{{256 \times 3.14}}{3} \\
= 267.95{\left( {mm} \right)^3} \\
\]
Hence, the volume of the sphere is 267.95 cubic milli-meters.
Note: To find the capacity of a closed curve/body, the volume is calculated for a three-dimensional object, and the area is calculated for a two-dimensional figure. The three-dimensional sphere is obtained when a two-dimensional circle is rotated about its symmetry.
Recently Updated Pages
what is the correct chronological order of the following class 10 social science CBSE
Which of the following was not the actual cause for class 10 social science CBSE
Which of the following statements is not correct A class 10 social science CBSE
Which of the following leaders was not present in the class 10 social science CBSE
Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE
Which one of the following places is not covered by class 10 social science CBSE
Trending doubts
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Difference Between Plant Cell and Animal Cell
Why is there a time difference of about 5 hours between class 10 social science CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Draw a labelled sketch of the human eye class 12 physics CBSE