Question

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Answer 1

Radius of cone is 6 cm

Explanation:

`\sf\small\underline\purple{Given:-}`

`\sf{\leadsto Volume\:_((cone))=120π \:cm^3}`

`\sf{\leadsto \: Height\:_((cone))=10 cm}`

`\sf\small\underline\purple{To\: Find:-}`

`\sf{\leadsto Radius\:_((cone))=?}`

`\sf\small\underline\purple{Solution:-}`

To calculate the radius of cone . Simply by applying formula of volume of cone. As given in the question that height is 10 cm and it's volume is 120 π cm³.

`\sf\small\underline\purple{Calculation\: begin:-}`

`\sf{\leadsto Volume\:_((cone))=(1)/(3)\pi\:r^2\:h}`

`\small \sf \leadsto volume \: of \: cone \: = (1)/(3) \pi * r {}^(2) h \\`

`\small \sf \leadsto \: 120 π cm³ \: = (1)/(3) *\pi r {}^(2) * 10cm \\`

`\small \sf \leadsto \: 120 π cm³ \: = (10 \: \pi\: cm)/(3) \: r {}^(2)`

`\small \sf \leadsto \frac{ 120\pi \: cm {}^(3) * 3}{10\pi \: cm} \: = r {}^(2) \\ \\`

`\small \sf \leadsto \frac{360\pi cm {}^(3) }{10\pi \: cm} = \: r {}^(2) \\`

`\small \sf \leadsto 36 \:cm {}^(2) = r {}^(2)`

`\small \sf \leadsto \sqrt{36 \: cm {}^(2) } = \sqrt{r {}^(2) }`

`\small \sf \leadsto6cm = r`

Answer 2

`\displaystyle r = 6 \ cm`

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Equality Properties

• Multiplication Property of Equality
• Division Property of Equality
• Addition Property of Equality
• Subtraction Property of Equality

Geometry

Volume of a Cone Formula:
`\displaystyle V = (\pi)/(3)r^2h`

• r is radius
• h is height

Explanation:

Step 1: Define

Identify variables

V = 120π cm³

h = 10 cm

Step 2: Solve for r

1. Substitute in variables [Volume of a Cone Formula]:
   `\displaystyle 120\pi \ cm^3 = (\pi)/(3)r^2(10 \ cm)`
2. Multiply:
   `\displaystyle 120\pi \ cm^3 = (10\pi)/(3)r^2 \ cm`
3. [Division Property of Equality] Divide
   `\displaystyle (10\pi)/(3) \ cm` on both sides:
   `\displaystyle 36 \ cm^2 = r^2`
4. [Equality Property] Square root both sides:
   `\displaystyle 6 \ cm = r`
5. Rewrite:
   `\displaystyle r = 6 \ cm`