Respuesta :

Space

Answer:

[tex]\displaystyle r = 6 \ cm[/tex]

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: [tex]\displaystyle V = \frac{\pi}{3}r^2h[/tex]

  • r is radius
  • h is height

Step-by-step 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]:                                    [tex]\displaystyle 120\pi \ cm^3 = \frac{\pi}{3}r^2(10 \ cm)[/tex]
  2. Multiply:                                                                                                             [tex]\displaystyle 120\pi \ cm^3 = \frac{10\pi}{3}r^2 \ cm[/tex]
  3. [Division Property of Equality] Divide  [tex]\displaystyle \frac{10\pi}{3} \ cm[/tex]  on both sides:                      [tex]\displaystyle 36 \ cm^2 = r^2[/tex]
  4. [Equality Property] Square root both sides:                                                    [tex]\displaystyle 6 \ cm = r[/tex]
  5. Rewrite:                                                                                                             [tex]\displaystyle r = 6 \ cm[/tex]

Answer:

Radius of cone is 6 cm

Step-by-step explanation:

[tex]\sf\small\underline\purple{Given:-}[/tex]

[tex]\sf{\leadsto Volume\:_{(cone)}=120π \:cm^3}[/tex]

[tex]\sf{\leadsto \: Height\:_{(cone)}=10 cm}[/tex]

[tex]\sf\small\underline\purple{To\: Find:-}[/tex]

[tex]\sf{\leadsto Radius\:_{(cone)}=?}[/tex]

[tex]\sf\small\underline\purple{Solution:-}[/tex]

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.

[tex]\sf\small\underline\purple{Calculation\: begin:-}[/tex]

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

[tex] \small \sf \leadsto volume \: of \: cone \: = \frac{1}{3} \pi \times r {}^{2} h \\ [/tex]

[tex] \small \sf \leadsto \: 120 π cm³ \: = \frac{1}{3} \times\pi r {}^{2} \times 10cm \\[/tex]

[tex] \small \sf \leadsto \: 120 π cm³ \: = \frac{10 \: \pi\: cm}{3} \: r {}^{2}[/tex]

[tex] \small \sf \leadsto \frac{ 120\pi \: cm {}^{3} \times 3}{10\pi \: cm} \: = r {}^{2} \\ \\ [/tex]

[tex] \small \sf \leadsto \frac{360\pi cm {}^{3} }{10\pi \: cm} = \: r {}^{2} \\ [/tex]

[tex]\small \sf \leadsto 36 \:cm {}^{2} = r {}^{2} [/tex]

[tex]\small \sf \leadsto \sqrt{36 \: cm {}^{2} } = \sqrt{r {}^{2} } [/tex]

[tex]\small \sf \leadsto6cm = r[/tex]

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