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CBSE Class 9 Answered

Respected Sir/Madam<

Kindly provide me the detailed explanation to the question

1.   1. If the edge of cube is increased by 25%, then find the percentage increase in its surface area.

2.   2. If the radius of a sphere is doubled, its volume will become how many times its original volume?

Asked by apoorva2000ojha | 07 Jan, 2015, 07:46: PM
answered-by-expert Expert Answer
1. space l e t space t h e space e d g e space o f space t h e space c u b e space b e space apostrophe a apostrophe. T o t a l space S u r f a c e space a r e a space o f space t h e space c u b e space equals space 6 a squared N e w space e d g e space o f space t h e space c u b e space equals space a plus 25 % o f space a space equals space a space plus space 25 over 100 cross times a equals a space plus space 1 fourth cross times a equals a plus space a over 4 equals fraction numerator 4 a plus a over denominator 4 end fraction equals fraction numerator 5 a over denominator 4 end fraction N e w space T o t a l space S u r f a c e space a r e a space o f space t h e space c u b e space equals 6 cross times space open parentheses fraction numerator 5 a over denominator 4 end fraction close parentheses squared equals 6 cross times fraction numerator 25 a squared over denominator 16 end fraction equals fraction numerator 150 a squared over denominator 16 end fraction P e r c e n t a g e space i n c r e a s e space i n space i t s space s u r f a c e space a r e a space equals space fraction numerator N e w space T S A minus O r i g i n a l space T S A over denominator O r i g i n a l space T S A end fraction cross times 100 equals space fraction numerator fraction numerator 150 a squared over denominator 16 end fraction minus 6 a squared over denominator 6 a squared end fraction cross times 100 equals fraction numerator begin display style fraction numerator 150 a squared minus 96 a squared over denominator 16 end fraction end style over denominator 6 a squared end fraction cross times 100 equals fraction numerator begin display style fraction numerator 54 a squared over denominator 16 end fraction end style over denominator 6 a squared end fraction cross times 100 equals fraction numerator 54 a squared over denominator 16 cross times 6 a squared end fraction cross times 100 equals 56 1 fourth % I n c r e a s e space i n space t h e space s u r f a c e space a r e a space equals space 56 1 fourth % P l e a s e space p o s t space o n l y space o n e space q u e s t i o n space i n space e a c h space q u e r y.
Answered by Prasenjit Paul | 08 Jan, 2015, 08:25: AM
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