Answer:
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: [tex]\displaystyle V = \frac{\pi r^2 h}{3}[/tex]
Diameter of a Circle Formula: [tex]\displaystyle d = 2r[/tex]
Step-by-step explanation:
Step 1: Define
Identify variables.
[tex]\displaystyle V = 56.52 \ \text{in}^3 \\h = 6 \ \text{in}[/tex]
Step 2: Find Diameter
∴ we find the diameter to be 6 inches.
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Topic: Algebra I/Geometry A
[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]
heya! ^^
given ,
[tex] Volume \: of \: cube = 56.52 \: inches^{3} \\ \\ Height \: of \: cone = 6 inches \\ [/tex]
now ,
[tex]\bold\purple{Volume \: of \: cube = \frac{1}{3} \pi r^{2} h }\\ \\ \implies 56.52 = \frac{1}{\cancel{3}} \times \frac{22}{7} \times r^{2} \times \cancel{6} \\ \\ \implies r^{2} = \frac{ 56.52 \times 7}{22 \times 2} \\ \\ \implies r^{2} = \frac{395.64}{44} \\ \\ \implies r^{2} = 9\: inches ( approx. ) \\ \\ \implies \bold\pink{r = 3 \: inches}\\ [/tex]
now ,
diameter , D = 2r
[tex]\dashrightarrow D = 2 \times 3 \\ \\ \dashrightarrow \bold\red{D = 6 \:inches} \\ [/tex]
hope helpful :D
