Question

1. The volume of cone is 18480 cubic cm if the height of the cone is 40 cm find the radius of the base​

Answer 1

Answer:

$\sf\large\underline\red{Given:}$

The volume of cone is 18480 cubic cm

The height of the cone is 40 cm.

$\sf\large\underline\red{To\:find:}$

Find the radius of the base.

$\sf\large\underline\red{Solution:}$

Let the radius of the cone be ' r ' cm

Height ( h ) = 40 cm

Volume ( v ) = 18480 cm³

We know that,

$\boxed{\bf{\blue{Volume\:of\:a\:right\:circular\:cone\:=\dfrac{1}{3}πr²h}}}$

Where,

v ⭆ Volume

r ⭆ The radius of Circular Base

h ⭆ height of cone

π ⭆22/7

$\sf\green{★\:According\:to\:the\:question}$

$\sf{\implies \dfrac{1}{3} × 1×π×r²×40=18480}$

$\sf{\implies \dfrac{1}{3} × \dfrac{22}{7} × r² × 40 = 18480}$

$⟹31×722×r²×40=18480$

$\sf{\implies r² × \dfrac{880}{21} = 18480}⟹r²×21880=18480$

$\sf{\implies r² = 18480 × \dfrac{21}{880}}⟹r²=18480×88021$

$\sf{\implies r² = 21×21}⟹r²=21×21$

$\sf{\implies r² = 441}⟹r²=441$

$\sf{\implies r = 21}⟹r=$21

Therefore,

The radius of the base of the cone is 21 cm .