Question

100 POINTS

A cone has a slant height of 7.5cm and a radius of 4.5 cm. What is the volume of the cone?

Answer 1

• h²=7.5²-4.5²
• h²=6²
• h=6cm

Now

volume:-

• 1/3πr²h
• 1/3π(4.5)²(6)
• π(20.25)(2)
• 40.5πcm³

Answer 2

• Volume of cone = 127.17 cm³

Explanation:

In the question we are given ,

• Slant height = 7.5 cm

• Radius = 4.5 cm

And we are asked to find the volume of cone. We know that ,

`\red{\boxed{ \rm{Volume \: of \: cone = (1)/(3) \pi r {}^(2)h }}}`

Where ,

• π = 3.14

• r = 4.5 cm

• h = Not given

So , for finding volume of cone we must have to find the height of cone using slant height formula i.e. ,

`\green{\boxed{ \sf{l {}^(2) = h {}^(2) + r {}^(2) }}}`

Where ,

• l = slant height

• h = height

• r = radius

Now , substituting values :

`\hookrightarrow \: 7.5 {}^(2) = h {}^(2) + 4.5 {}^(2)`

Transposing 4.5 to left hand side :

`\hookrightarrow \: 7.5 {}^(2) - 4.5 {}^(2) = h {}^(2)`

`\hookrightarrow \:56.25 - 20.25 = h {}^(2)`

On further calculations we get :

`\hookrightarrow \:h {}^(2) = 36`

`\hookrightarrow \:h = √(36)`

We know that 6 × 6 is equal to 36 that means square root of 36 is 6 . So :

`\hookrightarrow \pink{\boxed{\bold{h = 6 \: cm}}}`

• Therefore, height of cylinder is 6 cm .

Now finding volume :

Substituting values in volume formula :

`\longrightarrow\: \frac{1}{ \cancel{3} } * 3.14 * (4.5) {}^(2) * \cancel{6}`

Step 1 : By cancelling 6 with 3 we get :

`\longrightarrow \: 3.14 * 20.25 * 2`

Step 2 : Multiplying 20.25 with 2 :

`\longrightarrow \:3.14 * 40.50`

Step 3 : Multiplying 3.14 with 40.50 :

`\longrightarrow \: \purple{\boxed{\bold{127.17 \: cm {}^(3) }}}`

• Therefore, volume of cone is 127.17 cm³ .

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