1c:I[1254,["7330","static/chunks/d3ac728e-78c3d5d7a486ed3a.js","5159","static/chunks/5159-48592f0bf1a47f9d.js","8175","static/chunks/8175-f84d59b9bd013e10.js","8167","static/chunks/8167-b25693a0140130f2.js","664","static/chunks/664-bceb0f356f9312eb.js","3703","static/chunks/app/practice-question/%5Bslug%5D/page-d1408559b663b83f.js"],"PracticeQuestionCard"] 1b:T481,{"@context":"https://schema.org","@type":"QAPage","name":"A sphere and a cube have equal surface area. The ratio of the volume…","url":"https://vidyalelo.com/practice-question/a-sphere-and-a-cube-have-equal-surface-area-the-ratio-of-the-volume-of-the-sphere-to-that-of-the-cube-is-109858","keywords":"practice questions, MCQ, MCQs with answers, objective questions, competitive exam questions, Competitive Exams, Competitive Exams MCQ, Competitive Exams MCQs, Competitive Exams questions, Competitive Exams practice questions, Aptitude, Aptitude MCQ, Aptitude MCQs, Aptitude questions, Aptitude practice questions, Volume And Surface Area","mainEntity":{"@type":"Question","name":"A sphere and a cube have equal surface area. The ratio of the volume…","text":"A sphere and a cube have equal surface area. The ratio of the volume of the sphere to that of the cube is :","answerCount":1,"acceptedAnswer":{"@type":"Answer","text":"Option D. 6 :. Answer & Solution Answer: Option D Solution: & 4 R^2 = 6a^2 & R^2a^2 = 32 & R/a = 3 2 & Volume of spere Volume of cube & = 4/3 R^3a^3 & = 4/3 ( R/a )^3 & = 4/3 3 3 2 2 & = 2 3 2 & = 12 2 & = 6 & or, 6 :"}}}1d:T444,

Answer & Solution

Answer: Option D

Solution:

$$\eqalign{ & 4\pi {R^2} = 6{a^2} \cr & \Rightarrow \frac{{{R^2}}}{{{a^2}}} = \frac{3}{{2\pi }} \cr & \Rightarrow \frac{R}{a} = \frac{{\sqrt 3 }}