# CAT Quantitative Aptitude Questions | CAT Geometry - Mensuration Problems

###### CAT Questions | CAT Mensuration Questions | Spheres
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This question is from CAT Mensuration in CAT Geometry. In this Question, A sphere is cut into two pieces and its cumulative surface area increases. We need to find the height. Mensuration Questions in the CAT exam can be solved with practical approach and thought process rather than just knowing theorems from CAT Geometry. Even if one is not completely prepared for CAT Geometry exam, he or she should be able to do well in Mensuration problems tested by the CAT Exam. Knowing Mensuration formulas is important. Make sure you master Mensuration questions for CAT exam. Cutting a sphere into two equal parts increases its surface area by 50%, what will be the increase if we cut it in some other fashion?

Question 2: A sphere of radius r is cut by a plane at a distance of h from its center, thereby breaking this sphere into two different pieces. The cumulative surface area of these two pieces is 25% more than that of the sphere. Find h.

1. $$frac{r}{√2}\\$ 2. $\frac{r}{√3}\\$ 3. $\frac{r}{√5}\\$ 4. $\frac{r}{√6}\\$ ## 2IIM : Best Online CAT Coaching #### Signup and sample 9 full classes for free The Best CAT Online Coaching Courses ### Video Explanation ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2020Starts Sun, March 1st, 2020 ### Explanatory Answer ##### Method of solving this CAT Question from Geometry - Mensuration: Visualising the question and understanding of the surface area formula is the key to answer. Area = 4πr2 Cumulative area of the two pieces = 25% more than that of sphere. Area of 2 pieces = 1.25 × 4π2 = 5πr2 Extra area = πr2 Extra area = area of two new circles that are now created circles. Area each new circle = $\frac{πr^2}{2}\\$ Let radius of new circle be r1. Now, πr12 = $\frac{πr^2}{2}\\$ r1 = $\frac{r}{√2}\\$ Now, r1 , h and r form a right angled triangle. h2 + r12 = r2 h2 +$$$frac{r}{√2}\\$)2 = r2 h = $\frac{r}{√2}\\$ Choice$A) is therefore, the correct answer.

The question is " The cumulative surface area of these two pieces is 25% more than that of the sphere. Find h. "

##### Hence, the answer is $$frac{r}{√2}\\$ Choice A is the correct answer. ###### Signup and sample 9 full classes for free The Best Online CAT Coaching Courses. Signup ! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2020Enroll at 44,000/- Next Weekend Batch Starts Sun, March 1st 2020 ###### Best CAT Coaching in ChennaiRegister Online, get Rs 4000/- off Attend a Demo Class ## CAT Preparation Online | CAT Geometry - Mensuration Videos On YouTube #### Other useful sources for Geometry Questions | Mensuration Questions ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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