contestada

Marti is filling a 10– inch diameter ball with sand to make a medicine ball that can be used for exercising. To determine if the medicine ball will be too heavy after it is completely full of sand, she did some research and found that there is approximately 100 pounds of sand per cubic foot. How heavy will the medicine ball be after it is filled with sand, rounded to the nearest pound? A.30 pounds B.58 pounds C.24 pounds D.83 pounds

Respuesta :

calculista

Answer:

Option A. [tex]30\ pounds[/tex]

Step-by-step explanation:

step 1

Find the volume of the sphere ( medicine ball)

The volume is equal to

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

we have

[tex]r=10/2=5\ in[/tex] ----> the radius is half the diameter

Convert inches to feet

Remember that

1 ft=12 in

[tex]r=5\ in=5/12\ ft[/tex]

assume

[tex]\pi=3.14[/tex]

substitute

[tex]V=\frac{4}{3}(3.14)(5/12)^{3}[/tex]

[tex]V=0.3029\ ft^{3}[/tex]

step 2

Find the weight of the ball

Multiply the volume in cubic foot by 100

[tex]0.3029*100=30.29\ pounds[/tex]

Round to the nearest pound

[tex]30.29=30\ pounds[/tex]

oladayoademosu

The medicine ball would be A. 30 pounds

Volume of the medicine ball

Since the medicine ball is a sphere, its volume is

V = πd³/6 where d = diameter of medicine ball = 10 in = 10 in × 1 ft/12 in = 0.8333 ft

So, substituting the value of the variable into the equation, we have

V = πd³/6

V = π(0.8333 ft)³/6

V = π(0.5787 ft³)/6

V = 1.818 ft³/6

V = 0.303 ft³

Mass of medicine ball

The mass of the medicine ball = mass of sand per cubic foot × volume of medicine ball

where

  • mass of sand per cubic foot = 100 lb/ft³ and
  • volume of medicine ball = 0.303 ft³

So,

mass of the medicine ball = 100 lb/ft³ × 0.303 ft³

= 30.3 lb

≅ 30 pounds

So, the medicine ball would be A. 30 pounds

Learn more about mass of sphere here:

https://brainly.com/question/8765505