If a hemisphere of radius 21 cm is melted and recast to form a cone of height 42 cm, then the radius of cone is ___.

10 cm

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16 cm

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14 cm

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21 cm

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Solution

The correct option is D 21 cm
Given: Radius of the hemisphere = 21 cm
Height of the cone is = 42 cm
Let the radius of the cone be r.
Volume of cone = Volume of hemisphere
$\frac{1}{3} π \times r^{2} \times 42 = \frac{2}{3} π \times 21 \times 21 \times 21$
$r^{2} = 21^{2}$
r = 21 cm

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If a hemisphere of radius 21 cm is melted and recast to form a cone of height 42 cm, then the radius of cone is ___.

The correct option is D 21 cmGiven: Radius of the hemisphere = 21 cm Height of the cone is = 42 cm Let the radius of the cone be r. Volume of cone = Volume of hemisphere 13 π ×r2 × 42=23π × 21 × 21 × 21 r2=212 r = 21 cm

The correct option is D 21 cm
Given: Radius of the hemisphere = 21 cm
Height of the cone is = 42 cm
Let the radius of the cone be r.
Volume of cone = Volume of hemisphere
$\frac{1}{3} π \times r^{2} \times 42 = \frac{2}{3} π \times 21 \times 21 \times 21$
$r^{2} = 21^{2}$
r = 21 cm