Answer
Verified
376.5k+ views
Hint: First we have to define what the terms we need to solve the problem are.
Since we need to find the radius of the sphere, and things we need to know about circumference first which is the perimeter of the given circle or else like the ellipse. And the solid content is the total amount of the base product. sphere radius that we need to find using $V = \dfrac{{4\pi {r^3}}}{3}$(pie is twenty two divides seven)
Complete step-by-step solution:
Thus, we need to find the radius of the sphere for the given problem and let take or assume that $r$is the radius of the sphere, so that it will useful in the calculation purpose;
Now since the radius is half of the diameter. And the sphere radius is known as r which has to find using the $V = \dfrac{{4\pi {r^3}}}{3}$ and also that $2\pi r$ is the circumference of a given circle or perimeter with the radius $r$.
To find the same numerical value we just need to equals to above two known values and find the radius for it; which means $\dfrac{{4\pi {r^3}}}{3} = 2\pi r$(to find the radius of the sphere for same numerical value so we equivalent that both equations)
Hence solving further, we can able to obtain; $\dfrac{{4\pi {r^3}}}{3} = 2\pi r \Rightarrow \dfrac{{4{r^2}}}{3} = 2$(both sides pie and r will cancel each other) and hence $ \Rightarrow \dfrac{{4{r^2}}}{3} = 2 \Rightarrow {r^2} = \dfrac{{2 \times 3}}{4}$(cross multiplying we get)
Hence, we get ${r^2} = 1.5$(now taking square roots on the both we get in left side only r as the radius so we are doing that)
Thus ${r^2} = 1.5 \Rightarrow r = 1.22$which is the required radius of the sphere whose circumference and the solid content have the same numerical value as well as.
Note: since radius of the sphere is $V = \dfrac{{4\pi {r^3}}}{3}$and circumference of the given circle or perimeter is $2\pi r$
Also, radius means half of the given diameter in the circle or sphere; numerical means the radius will need to be shown as the number value.
Since we need to find the radius of the sphere, and things we need to know about circumference first which is the perimeter of the given circle or else like the ellipse. And the solid content is the total amount of the base product. sphere radius that we need to find using $V = \dfrac{{4\pi {r^3}}}{3}$(pie is twenty two divides seven)
Complete step-by-step solution:
Thus, we need to find the radius of the sphere for the given problem and let take or assume that $r$is the radius of the sphere, so that it will useful in the calculation purpose;
Now since the radius is half of the diameter. And the sphere radius is known as r which has to find using the $V = \dfrac{{4\pi {r^3}}}{3}$ and also that $2\pi r$ is the circumference of a given circle or perimeter with the radius $r$.
To find the same numerical value we just need to equals to above two known values and find the radius for it; which means $\dfrac{{4\pi {r^3}}}{3} = 2\pi r$(to find the radius of the sphere for same numerical value so we equivalent that both equations)
Hence solving further, we can able to obtain; $\dfrac{{4\pi {r^3}}}{3} = 2\pi r \Rightarrow \dfrac{{4{r^2}}}{3} = 2$(both sides pie and r will cancel each other) and hence $ \Rightarrow \dfrac{{4{r^2}}}{3} = 2 \Rightarrow {r^2} = \dfrac{{2 \times 3}}{4}$(cross multiplying we get)
Hence, we get ${r^2} = 1.5$(now taking square roots on the both we get in left side only r as the radius so we are doing that)
Thus ${r^2} = 1.5 \Rightarrow r = 1.22$which is the required radius of the sphere whose circumference and the solid content have the same numerical value as well as.
Note: since radius of the sphere is $V = \dfrac{{4\pi {r^3}}}{3}$and circumference of the given circle or perimeter is $2\pi r$
Also, radius means half of the given diameter in the circle or sphere; numerical means the radius will need to be shown as the number value.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE