Question

A sphere of radius 10.5cm is melted and then recast into small cones each of radius 3.5cm and height 3cm.The number of cones formed is .

Answer 1

ANSWER:

• The number of cones made = 126.

GIVEN:

• A sphere is melted and then recast into small cones.

• Radius of sphere = 10.5 cm.

• Radius and height of cone are 3.5 cm and 3 cm respectively.

TO FIND:

• The number of cones made.

EXPLANATION:

Diagram(Sphere):

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0) \thicklines\qbezier( - 1.115,0)( - 1,1)(0,1.115)\qbezier(1.115,0)(1,1)(0, 1.115)\qbezier( - 1.115,0)( - 1, - 1)(0, - 1.115)\qbezier(0, - 1.115)( 1, - 1)(1.115,0) \put( - 0.1,0){\line(1,0) {1.2}} \put(0.3,0.1){ \bf r_1 } \put( - 0.2,0){ \circle*{ 0.1}}\end{picture}$

Volume of sphere = 4/3 πr₁³

r₁ = 10.5 cm

Diagram(Cone):

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0) \thicklines\qbezier( - 1,0)( - 1,0)(0.3,3)\qbezier(2,0)(2,0)(0.3, 3)\qbezier( - 1,0)( 0.4, - 1.2)(2, 0)\qbezier( - 1,0)( 0.4,1.2)(2, 0) \put(0.2,0){ \line( 0,1){3}}\put(0.2,0){ \line(1,0){1.7}} \put(0.8,0.1){ \bf r_2 }\put( - 0.1,0.8){ \bf h }\end{picture}$

Volume of cone = 1/3 πr₂²h

r₂ = 3.5 cm

h = 3 cm

Volume of sphere = n × Volume of cone

[ As sphere is melted into cones ]

4/3 π(10.5)³ = n × 1/3 π(3.5)² × 3

4 × 10.5 × 10.5 × 10.5 = n × 3.5 × 3.5 × 3

4 × 10.5 × 10.5 × 3 = n × 10.5

12 × 10.5 = n

n = 126

HENCE 126 CONES CAN BE MADE.

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0) \multiput(0,0)(1,0){7}{\line(1,0){0.5}}\multiput(0, - 0.14)(1,0){7}{\line(1,0){0.5}} \put( - 0.1, - 0.14){ \line(0, 1){0.14}} \linethickness{1.4mm}\multiput(0.5, - 0.07)(1,0){7}{\line(1,0){0.5}}\end{picture}$

Answer 2

Answer:

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