Ask a Doubt
Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 10 Answered

A metallic sphere of diameter 1cm is to be melted & recasted into a hollow sphere of thickness 1mm. Find the internal & external radii of the sphere.
Asked by araima2001 | 23 Nov, 2015, 10:26: AM
answered-by-expert Expert Answer
begin mathsize 14px style Given colon Diameter space of space solid space sphere space equals space 1 space cm space therefore Radius space of space solid space sphere space equals space 0.5 space cm equals space 5 space mm Volume space of space solid space sphere space equals space 4 over 3 straight pi space straight r cubed equals space 4 over 3 straight pi space 5 cubed space space space... left parenthesis 1 right parenthesis Let space straight r subscript 1 space be space internal space radius space of space hollow space sphere Let space straight r subscript 2 space be space external space radius space of space hollow space sphere As space per space the space given space information comma space straight r subscript 2 space minus straight r subscript 1 space equals space 1 space mm space space therefore straight r subscript 2 space equals space straight r subscript 1 plus 1 space space space... space left parenthesis 2 right parenthesis Volume space of space hollow space sphere space equals space 4 over 3 straight pi space straight r subscript 2 cubed space minus space 4 over 3 straight pi space straight r subscript 1 cubed space Here space Volume space of space solid space sphere space equals Volume space of space hollow space space sphere space therefore 4 over 3 straight pi space 5 cubed space equals space 4 over 3 straight pi space straight r subscript 2 cubed space minus space 4 over 3 straight pi space straight r subscript 1 cubed space therefore 4 over 3 straight pi space 5 cubed space equals space space 4 over 3 straight pi open parentheses straight r subscript 2 cubed space minus straight r subscript 1 cubed space close parentheses therefore 125 space equals space open parentheses straight r subscript 2 cubed space minus straight r subscript 1 cubed space close parentheses therefore open parentheses straight r subscript 2 space minus space straight r subscript 1 close parentheses space open parentheses straight r subscript 2 squared plus straight r subscript 1 straight r subscript 2 plus straight r subscript 1 squared close parentheses equals space 125 space space space space Substituting space straight r subscript 2 space minus straight r subscript 1 space equals space 1 comma therefore space open parentheses straight r subscript 2 squared plus straight r subscript 1 straight r subscript 2 plus straight r subscript 1 squared close parentheses equals space 125 space space space... left parenthesis 3 right parenthesis space Substituting comma straight r subscript 2 space equals space straight r subscript 1 plus 1 space in open parentheses 3 close parentheses space space space space end style
 
begin mathsize 14px style therefore space space open parentheses space straight r subscript 1 plus 1 close parentheses squared plus straight r subscript 1 open parentheses straight r subscript 1 plus 1 close parentheses plus straight r subscript 1 squared space equals space 125 therefore straight r subscript 1 squared plus 2 straight r subscript 1 plus 1 plus straight r subscript 1 squared plus straight r subscript 1 plus straight r subscript 1 squared space equals space 125 therefore 3 straight r subscript 1 squared space plus 3 straight r subscript 1 plus 1 equals 125 therefore 3 straight r subscript 1 squared space plus 3 straight r subscript 1 minus 124 space equals space 0 therefore straight r subscript 1 space equals 5.9 space or space minus space 6.9 Radius space can space not space be space negative therefore straight r subscript 1 equals Internal space radius space equals space 5.9 space mm straight r subscript 2 space equals External space radius space equals straight r subscript 1 plus 1 space equals 5.9 plus 1 equals space 6.9 space mm end style
Answered by Priti Shah | 23 Nov, 2015, 02:28: PM

Application Videos

Concept Videos

Multiple Choice Questions Practice Test
Answered Unanswered My Questions My Answers
CBSE 10 - Maths
what is cone surface area
Asked by sagarvarun6535 | 03 Mar, 2024, 09:37: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
find the height of largest right circular cone that can be cut out of a cube whose volume is 729 cm³
Asked by jogindersingh7065929020 | 20 Jan, 2024, 09:29: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
a company wanted to manufacture 1000 hemispheres basins from thin steel sheet radius is 21 cm find the required area of steel sheet manufacturers the above hemispherical basins
Asked by barakaakashgoud | 21 Dec, 2023, 05:16: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
A rocket is in the form of circular closed at the ler end and a cone of same radius is attached to the top.The radius of the clylinder is 2.5m ,it's height is 21m and the slant height of the cone is 8m Find the T.S.A of rocket
Asked by ybproduction256 | 27 Nov, 2023, 12:26: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
a wooden toy rocket is in the shape of cone mounted on a cylinder. The height of the entire rocket is 15 cm, while the height of the conical part is 4 cm. The base of the conical portion has a diameter of 6 cm, while the base diameter of the cylindrical portion is 4 cm. If the conicle portion is painted green and the cylindrical portion is painted blue, find the area of the rocket. (use π=3.14)
Asked by shivalaxmi0205 | 05 Sep, 2023, 06:55: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
A golf ball is spherical with about 300 - 500 dimples that help increase its velocity while in play. Golf balls are traditionally white but available in colours also. In the given figure, a golf ball has diameter 4-2 cm and the surface has 315 dimples (hemi-spherical) of radius 2 mm. Based on the above, answer the following questions: (i) Find the surface area of one such dimple. (ii) Find the volume of the material dug out to make one dimple. Find the total surface area exposed to the surroundings.
Asked by swetalinasamantaray022 | 21 Mar, 2023, 04:16: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
If radius of the base of cone is 7 cm and height is 24 cm, then find its slant height. (A) 23 cm  (B) 26 cm  (C) 31 cm  D) 25 cm
Asked by rashmij34 | 18 Mar, 2023, 11:03: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
8th one
question image
Asked by pentikalyanram | 22 Dec, 2022, 08:12: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
3. A glass cylinder with radius 10 cm has water to a height of 9 cm. A metal cube of 8 cm edge is immersed in it completely. Calculate the height by which water will rise in the cylinder. Use =22/7
Asked by rajsingh94116633 | 04 May, 2022, 10:06: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
A conical tank with base radius 20 cm and height 40 cm is initially filled with water. Water drains through a small round hole at the bottom with a diameter of 1cm. Find an expression for the height of water in the tank at time t  
Asked by anitajoshi0912 | 22 Dec, 2021, 09:12: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
My Class Videos Tests ₹ Plans Ask a Doubt
Get Latest Study Material for Academic year 24-25 Click here
×