Question

what is the diameter of a cone that has a volume of 56.52 cubic inches and a height of 6 inches. Use 3.14 for pi\

Answer 1

The diameter of the cone with the given volume and height is equal to 6 inches.

General Formulas and Concepts:
Geometry

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

• r is radius
• h is height

Diameter of a Circle Formula:
`\displaystyle d = 2r`

• r is radius

Explanation:

Step 1: Define

Identify variables.

`\displaystyle V = 56.52 \ \text{in}^3 \\h = 6 \ \text{in}`

Step 2: Find Diameter

1. [Volume of a Cone Formula] Substitute in variables:
   
   `\displaystyle 56.52 \ \text{in}^3 = \frac{\pi r^2 (6 \ \text{in})}{3}`
2. Solve for r:
   
   `\displaystyle r = 3 \ \text{in}`
3. [Diameter of a Circle Formula] Substitute in variables:
   
   `\displaystyle d = 2(3 \ \text{in})`
4. Evaluate:
   
   `\displaystyle d = 6 \ \text{in}`

∴ we find the diameter to be 6 inches.

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Topic: Algebra I/Geometry A

Answer 2

`\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}`

heya! ^^

given ,

`Volume \: of \: cube = 56.52 \: inches^(3) \\ \\ Height \: of \: cone = 6 inches \\`

now ,

`\bold\purple{Volume \: of \: cube = (1)/(3) \pi r^(2) h }\\ \\ \implies 56.52 = \frac{1}{\cancel{3}} * (22)/(7) * r^(2) * \cancel{6} \\ \\ \implies r^(2) = ( 56.52 * 7)/(22 * 2) \\ \\ \implies r^(2) = (395.64)/(44) \\ \\ \implies r^(2) = 9\: inches ( approx. ) \\ \\ \implies \bold\pink{r = 3 \: inches}\\`

now ,

diameter , D = 2r

`\dashrightarrow D = 2 * 3 \\ \\ \dashrightarrow \bold\red{D = 6 \:inches} \\`

hope helpful :D