Question

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Answer 1

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: $\displaystyle V = \frac{\pi}{3}r^2h$

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

Answer 2

Answer:

Radius of cone is 6 cm

Step-by-step 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.

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

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

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

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

$\small \sf \leadsto \: 120 π cm³ \: = \frac{10 \: \pi\: cm}{3} \: r {}^{2}$

$\small \sf \leadsto \frac{ 120\pi \: cm {}^{3} \times 3}{10\pi \: cm} \: = r {}^{2}$

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

$\small \sf \leadsto 36 \:cm {}^{2} = r {}^{2}$

$\small \sf \leadsto \sqrt{36 \: cm {}^{2} } = \sqrt{r {}^{2} }$

$\small \sf \leadsto6cm = r$