Question

A spherical tank has a radius of 6 yards. It is filled with a liquid that costs $7.15 per cubic yard. What is the total value of the liquid in the tank? Use 3.14 for π . Enter your answer in the box to the nearest cent.

Answer 1

Step 1

Find the volume of the tank

we know that

the volume of the sphere is equal to

$V=\frac{4}{3} \pi r^{3}$

where

r is the radius of the sphere

we have

$r=6\ yd$

substitute in the formula

$V=\frac{4}{3} \pi 6^{3}=904.32\ yd^{3}$

Step 2

Find the cost of the liquid

we know that

the cost of the liquid is $7.15\frac{\ }{yd^{3}}$

so

Multiply by the volume to obtain the total value of the liquid

$904.32\ yd^{3}*7.15\frac{\ }{yd^{3}}=\ 6,465.89$

therefore

the answer is

the total value of the liquid in the tank is $\ 6,465.89$

Answer 2

Answer:

Total value is $ 6465.89.

Step-by-step explanation:

Since, the volume of a sphere is,

$V=\frac{4}{3}\pi(r)^3$

Where, r is the radius of the sphere,

Here, the tank is of spherical shape having radius, r = 6 yards,

So, the volume of the tank is,

$V=\frac{4}{3}\pi (6)^3$

Since, $\pi = 3.14$

$\implies V=\frac{4}{3}\times 3.14\times 216=\frac{2712.96}{3}=904.32\text{ cube yards}$

Now, given,

The liquid in the tank costs $ 7.15 per cubic yards,

Hence, the total cost of the liquid in the given tank = cost of liquid cost per cubic yards × Volume of the tank

= 7.15 × 904.32

= $ 6465.888 ≈ $ 6465.89