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6 votes

Answer:

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

User Thanh DK
by
8.8k points
1 vote

Answer:


\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
User Francisco Souza
by
8.4k points

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