Question

A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recast into a shape. The radius of the sphere is: ​

Answer 1

Answer:

1/3*22/7*2.1*2.1*8.4=4/3*22/7*#

radius of sphere=2.1

Step-by-step explanation:

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Answer 2

Answer:

Radius of sphere is 2.1cm

Step-by-step explanation:

Given that

Height of cone is 8.4cm

Radius of base of cone is 2.1cm

It is recast in sphere

To find

Radius of sphere

Solution

Let

h is height of cone

rc as radius of cone.

rs as radius of sphere

vc as volume of cone

vs as volume of sphere

As we know that

$vc = \frac{1}{3} \pi \times {rc}^{2} \times h$

$vs = \frac{4}{3} \pi \times {rs}^{3}$

as it is recast then

$vc = vs$

hence

$\frac{1}{3} \pi \times {rc}^{2} \times h = \frac{4}{3} \pi \times {rs}^{3}$

$\pi \: will \: cancle \: from \: both \: side$

$\frac{1}{3} \pi \times (1.2 {)}^{2} \times 8.4 = \frac{4}{3} \times \pi \times {rs}^{3}$

by solving we get

$r {s}^{3} = 9.261$

as cube root of 9.261 is 2.1 hence

$rs = 2.1cm$

Hence radius of sphere is 2.1cm.