Question

Given a cone with the volume of 56.52 inches³ and height of 6 inches, then find its diameter​

Answer 1

Answer:

diameter = 6inches

Step-by-step explanation:

Given : volume = 56.52 inches³

height =6 inches

Find : diameter of cone

Formula used:

volume of cone = 1/3 πr²h

Solution :

volume of cone = 1/3 πr²h

56.52 inches³= 1/3 πr²× 6

56.52×3/ π= r²

56.52×3/3.14 = r²

2826/ 314= r²

9 = r²

3 = r

Therefore diameter = 2r = 2×4 =6inches

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Answer 2

Your Answer:

Given:-

• $\tt Volume \ \ of \ \ Cone = 56.52 \ inches^3$

• $\tt Height \ \ of \ \ Cone = 6 \ inches$

Solution:-

We know

$\tt Volume\ \ of \ \ a \ \ Cube = \dfrac{1}{3}\pi r^2 h$

So Replacing the values of Volume and Height

$\tt 56.52 = \dfrac{1}{3} (3.14) r^2(6) \\\\ \tt \Rightarrow \dfrac{56.52 \times 3}{3.14 \times 6} = r^2 \\\\ \tt \Rightarrow \dfrac{18 \times 3}{6} = r^2 \\\\ \tt \Rightarrow 3 \times 3 = r^2 \\\\ \tt \Rightarrow \sqrt{3 \times 3} = r \\\\ \tt \Rightarrow 3 =r$

We also know that $\tt 2Radius = Diameter$

So,

$\tt 2(3)= Diameter \\\\ \tt \Rightarrow 6inches =Diametre$

Other Formulas:

$\tt \underline {Volumes \ \ of \ \ Other \ \ 3D \ \ shapes}\\\\\\\tt \star Cuboid - l \times w \times h \\\\ \tt \star Sphere - (\dfrac{4}{3}) \pi r^3 \\\\ \tt \star Hemisphere - (\dfrac{2}{3}) \pi r^3 \\\\ \tt \star Cylinder - \pi r ^2 h$