Question

HELPPP! With a ruler, Diamond determines the diameter of a golf ball to be 4.2 centimeters (a radius of 2.1 cm) and the diameter of a practice softball to be 8.4 centimeters (a radius of 4.2 cm). Diamond erroneously claims that the softball has twice the volume of the golf ball. In a short paragraph, explain Diamonds misconceptions. Use the formula for the volume of a sphere to determine the volume of both the golf ball and the softball in cubic centimeters and then compare their volumes.
(Hint: Golf Ball Volume V = 4/3 π r3 ; V = 4/3 ∙ (3.14) ∙ (2.1)3 )

(Hint: Softball Volume V = 4/3 π r3 ; V = 4/3 ∙ (3.14) ∙ (4.2)3 )

Answer 1

Answer:

The softball has a volume which is 8 times the volume of the golf ball

Step-by-step explanation:

The volume of a sphere is:

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

The volume of the Golf ball is

$V= \frac{4}{3} \times 3.14 \times {(2.1)}^{3}$

$V= 38.77272 {cm}^{3}$

The volume of the soft ball is :

$V= \frac{4}{3} \times 3.14 \times {(4.2)}^{3}$

$V= 310.18176 {cm}^{3}$

To compare the volume s, we divide the volume of the softball by that of the golf ball:

$\frac{\frac{4}{3} \times 3.14 \times {(4.2)}^{3} }{\frac{4}{3} \times 3.14 \times {(2.1)}^{3} } = \frac{ {4.2}^{3} }{ {2.1}^{3} } = \frac{4.2 \times 4.2 \times 4.2}{2.1 \times 2.1 \times 2.1} = 2 \times 2 \times 2 = 8$

The softball has a volume which is 8 times the volume of the golf ball