Answer:
- Volume of cone = 127.17 cm³
Step-by-step explanation:
In the question we are given ,
And we are asked to find the volume of cone. We know that ,
[tex] \red{\boxed{ \rm{Volume \: of \: cone = \frac{1}{3} \pi r {}^{2}h }}}[/tex]
Where ,
So , for finding volume of cone we must have to find the height of cone using slant height formula i.e. ,
[tex] \green{\boxed{ \sf{l {}^{2} = h {}^{2} + r {}^{2} }}}[/tex]
Where ,
Now , substituting values :
[tex] \hookrightarrow \: 7.5 {}^{2} = h {}^{2} + 4.5 {}^{2} [/tex]
Transposing 4.5 to left hand side :
[tex] \hookrightarrow \: 7.5 {}^{2} - 4.5 {}^{2} = h {}^{2} [/tex]
[tex] \hookrightarrow \:56.25 - 20.25 = h {}^{2} [/tex]
On further calculations we get :
[tex] \hookrightarrow \:h {}^{2} = 36[/tex]
[tex] \hookrightarrow \:h = \sqrt{36} [/tex]
We know that 6 × 6 is equal to 36 that means square root of 36 is 6 . So :
[tex] \hookrightarrow \pink{\boxed{\bold{h = 6 \: cm}}}[/tex]
- Therefore, height of cylinder is 6 cm .
Now finding volume :
Substituting values in volume formula :
[tex] \longrightarrow\: \frac{1}{ \cancel{3} } \times 3.14 \times (4.5) {}^{2} \times \cancel{6}[/tex]
Step 1 : By cancelling 6 with 3 we get :
[tex] \longrightarrow \: 3.14 \times 20.25 \times 2[/tex]
Step 2 : Multiplying 20.25 with 2 :
[tex] \longrightarrow \:3.14 \times 40.50[/tex]
Step 3 : Multiplying 3.14 with 40.50 :
[tex] \longrightarrow \: \purple{\boxed{\bold{127.17 \: cm {}^{3} }}}[/tex]
- Therefore, volume of cone is 127.17 cm³ .
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