A sphere and a cube have …
CBSE, JEE, NEET, CUET
Question Bank, Mock Tests, Exam Papers
NCERT Solutions, Sample Papers, Notes, Videos
Posted by Sadhna Kashyap 8 years, 10 months ago
- 2 answers
Naveen Sharma 8 years, 10 months ago
Ans. Suppose radius of sphere is r and side of cube is x.
now,
Surface Area of Sphere = Surface Area of Cube
=> \(4 \times \pi \times r^2 = 6 \times x^2\)
=> \({ r^2 \over x^2} = {3 \over 2\pi}\)
=> \({r \over x } = {\sqrt{3 \over 2\pi}}\)
Let volume of Sphere = Vs
and volume of Cube = Vc
Then
=> \({V_s \over V_c} ={{{ 4 \over 3 }{ \pi r^3} } \over x^3}\)
=> \( {{4 \over 3 }\pi {({r \over x})^3}}\)
=> \( {{4 \pi \over 3} \times {3 \over 2\pi } \times \sqrt{3 \over 2\pi }}\)
=> \( \sqrt{12\over 2\pi}\)
=> \({{ \sqrt 6} \over {\sqrt \pi}}\)
So Required Ratio is = \(\sqrt 6 : \sqrt \pi \)
Test
Related Questions
Posted by Sheikh Alfaz 1 month, 2 weeks ago
- 0 answers
Posted by Savitha Savitha 1 year, 4 months ago
- 0 answers
Posted by Duruvan Sivan 6 months, 1 week ago
- 0 answers
Posted by Akhilesh Patidar 1 year, 4 months ago
- 0 answers
Posted by Yash Pandey 6 months, 1 week ago
- 0 answers
Posted by Alvin Thomas 3 months ago
- 0 answers
myCBSEguide
Trusted by 1 Crore+ Students
Test Generator
Create papers online. It's FREE.
CUET Mock Tests
75,000+ questions to practice only on myCBSEguide app
Rashmi Bajpayee 8 years, 10 months ago
According to question
4πr2 = 6a2
r2/a2 = 6/4π.
r/a = √3/√2π
Now ratio of their volumes
(4/3)πr3 / a3
= 4π/3 × (√3/√2π)3
= (4π/3)(3/2π)(√3/√2π)
= 2(3×7/2×22)
= √21/√11
Therefore ratio of their volumes is √21 : √11
0Thank You