Volumes Practice Test 1

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Question : 23 of 40

Marks: +1, -0

If the area of the base of a cone is 770

cm^2

and area of the curved surface is 814

cm^2

. Then find its volume.

$213 √5 cm^3$
$392 √5 cm^3$
$550 √5 cm^3$
$616√5 cm^3$

Solution:

Here,

πr^2

=770
⇒

r^2

=

{770×7}/{22}

∴ r =

√{35×7}

=

7√5

cm
and also πrl = 814
⇒

{22}/7 × 7√5 × l

= 814
∴ l =

{814}/{22×√5}

=

{37]/√5

cm
Since, h =

√{({37}/√5)&2-(7√5)^2}

=

√{{1369}/5-245}

=

√{{144}/5}

=

{12}/√5

cm
Hence, volume of the cone =

1/3 × {22}/7 × (7√5)^2 × {12}/√5

=

616√5 cm^3

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