Respuesta :
Answer:
24.8 ft
Step-by-step explanation:
Formula to find the volume of a sphere is :
Volume = [tex]\frac{4}{3}[/tex] π r³
Here,
r ⇒ radius
Given that,
Volume ⇒ 8000 ft³
Let us find the radius of the tank now.
Volume = [tex]\frac{4}{3}[/tex] π r³
8000 = [tex]\frac{4}{3}[/tex] π r³
8000 = [tex]\frac{4}{3}[/tex] × 3.14 × r³
8000 × 3 = 4 × 3.14 × r³
24000 = 12.56r³
Divide both sides by 12.56.
1910.822 = r³
∛1910.822 = r
12.40 ft = radius
And now let us find the diameter of the sphere.
d = 2r
d = 2 × 12.40
d = 24.8 ft
The diameter of the tank is 24.80 ft
Step-by-step explanation:
Given-
- A spherical tank holds 8,000 ft^3 of water
i.e. The volume of spherical tank = 8,000 ft^3
Now, the formula for finding volume of any spherical figure is-
[tex] \boxed{\mathfrak{ \purple{volume \:of \: sphere = \frac{4}{3} \pi {r}^{3} }}}[/tex]
Therefore, substituting value, we get
[tex]⇢8000 = \frac{4}{3} \pi {r}^{3} [/tex]
[tex]⇢8000 \times \frac{3}{4 } = \frac{22}{7} \pi {r}^{3} [/tex]
Transposing 4/3 to left hand side ,it will become 3/4 . And Here, 8000 will get cancelled by 4 leaving 2000
[tex]⇢2000 \times 3 \times \frac{7}{22} = {r}^{3} [/tex]
Similarly , On performing further calculations, we get. ..
[tex]⇢ \frac{21000}{11} = {r}^{3} [/tex]
[tex]⇢1910.822 = {r}^{3} [/tex]
[tex]⇢ \sqrt[3]{1910.822} = r[/tex]
[tex]⇢ \underline{12.40 = r}[/tex]
Thus, the radius of the tank is 12.40 ft
Now,
The diameter of the tank = 2 × radius
[tex] \: \: \: \: \: \: \: \: \: \: \: \: = 2 \times 12.40[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: = 24.80[/tex]
•°• The diameter of the tank comes out 24.80 ft
