Archive
21st of September 2015
Mathematics
Q:

the radius of sphere is 5 cm, if radius is increased by 20% find the % increase in volume and surface area?

Nisha_vini29 - CBSE - Class IX

Monday, September 21, 2015 at 14:45:PM

A:

R a d i u s space o f space s p h e r e equals 5 space c m P e r c e n t a g e space i n c r e a s e space i n space r a d i u s equals 20 percent sign A c t u a l space i n c r e a s e space i n space r a d i u s equals 20 over 100 cross times 5 equals 1 space c m N e w space r a d i u s equals 5 plus 1 equals 6 space c m V o l u m e space o f space t h e space s p h e r e comma space w h e n space r a d i u s i space straight s space 6 space c m equals 4 over 3 straight pi cross times 6 cubed V o l u m e space o f space t h e space s p h e r e comma space w h e n space r a d i u s i space straight s space 5 space c m equals 4 over 3 straight pi cross times 5 cubed I n c r e a s e space i n space v o l u m e equals 4 over 3 straight pi cross times 6 cubed minus 4 over 3 straight pi cross times 5 cubed space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 4 over 3 straight pi open parentheses 6 cubed minus 5 cubed close parentheses P e r c e n t a g e space i n c r e a s e space i n space V o l u m e equals fraction numerator 4 over 3 straight pi open parentheses 6 cubed minus 5 cubed close parentheses over denominator 4 over 3 straight pi cross times 5 cubed end fraction cross times 100 percent sign space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator open parentheses 6 cubed minus 5 cubed close parentheses over denominator 5 cubed end fraction cross times 100 percent sign space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 91 over 125 cross times 100 percent sign space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 72.8 percent sign S u r f a c e space a r e a space o f space t h e space s p h e r e comma space w h e n space r a d i u s i space straight s space 6 space c m equals 4 straight pi cross times 6 squared S u r f a c e space a r e a space o f space t h e space s p h e r e comma space w h e n space r a d i u s i space straight s space 5 space c m equals 4 straight pi cross times 5 squared I n c r e a s e space i n space S u r f a c e space a r e a equals 4 straight pi cross times 6 squared minus 4 straight pi cross times 5 squared space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 4 straight pi open parentheses 6 squared minus 5 squared close parentheses P e r c e n t a g e space i n c r e a s e space i n space S u r f a c e space a r e a equals fraction numerator 4 straight pi open parentheses 6 squared minus 5 squared close parentheses over denominator 4 straight pi cross times 5 squared end fraction cross times 100 percent sign space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator open parentheses 6 squared minus 5 squared close parentheses over denominator 5 squared end fraction cross times 100 percent sign space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 11 over 25 cross times 100 percent sign space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 44 percent sign

Monday, September 21, 2015 at 18:12:PM