Mensuration Practice Test 1

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Question : 12 of 40

Marks: +1, -0

A sphere and a hemisphere have the same volume. The ratio of their curved surface area is:

$2^{3/2} : 1$
$2^{2/3} : 1$
$4^{2/3} : 1$
$2^{1/3} : 1$

Solution:

Volume of sphere and hemisphere
=

4/3 πR^3

=

2/3 πr^3

=

2R^3

=

r^3

=

R^3/r^3

=

1/2

=

R/r

=

1/(2)^{1/3}

Ratio of their curved surface area is:

4π R^2 : 2π r^2

2R^2 : r^2

⇒

{2R^2}/r^2 : 1

⇒

{2(1)^2}/((2)^{1/3})^2 : 1

⇒

2/(2)^{2/3}

: 1
⇒

(2)^{1-2/3}

: 1

(2)^{1/3}

: 1

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