Round off to the nearest centimetre the diameter of a tennis ball is 7 cm and diameter of a football is 22 cm. Complete the calculation to find the difference between the two volume to the nearest centimetre (take π as 22/7)
The radius of the tennis ball is 7/2 = 3.5 cm.
The radius of the football is 22/2 = 11 cm.
The volume of the tennis ball is (4/3)π(3.5)^3 = 179.5945 cm^3.
The volume of the football is (4/3)π(11)^3 = 5575.2792 cm^3.
The difference between the two volumes is 5575.2792 - 179.5945 = 5395.6847 cm^3.
Rounding off to the nearest centimetre, the difference is 5396 cm^3.
The answer isn't clear enough
I apologize for the confusion.
To find the volume of the tennis ball, we use the formula for the volume of a sphere which is (4/3)πr^3, where r is the radius. Thus, the volume of the tennis ball is (4/3)π(3.5)^3 = 179.5945 cm^3 rounded to five decimal places.
To find the volume of the football, we use the same formula for the volume of a sphere, but with r = 11 cm. Thus, the volume of the football is (4/3)π(11)^3 = 5575.2792 cm^3 rounded to five decimal places.
To find the difference between the two volumes, we subtract the volume of the tennis ball from the volume of the football. Therefore, the difference is 5575.2792 cm^3 - 179.5945 cm^3 = 5395.6847 cm^3. Rounding off to the nearest centimetre, we get 5396 cm^3.
In the explanation above where did you get 3.5 and sine π is given why not use the fraction given as π to indicate
I apologize for the oversight in my previous response.
To find the volume of the tennis ball, we use the formula for the volume of a sphere which is (4/3)πr^3, where r is the radius of the tennis ball. The diameter of the tennis ball is given as 7 cm, so the radius is half of that value, which is 3.5 cm. Thus, the volume of the tennis ball is (4/3)π(3.5)^3 = 179.5945 cm^3 rounded to five decimal places.
For the volume of the football, the diameter is given as 22 cm, so the radius is half of that value, which is 11 cm. Using the value of π given as 22/7, the volume of the football is (4/3)(22/7)(11)^3 = 68040.8947 cm^3 rounded to five decimal places.
To find the difference between the two volumes, we subtract the volume of the tennis ball from the volume of the football. Therefore, the difference is 68040.8947 cm^3 - 179.5945 cm^3 = 67861.3002 cm^3. Rounding off to the nearest centimetre, we get 67861 cm^3.
Must every thing be decimal I am still little please break it down
I apologize for the confusion, let me break it down further.
The question provides us information about the diameter of a tennis ball and a football. The diameter is the distance across the ball. To find the radius of a sphere (which is half the diameter), we divide the diameter by 2. So, the radius of the tennis ball would be 7/2 = 3.5 cm, and the radius of the football would be 22/2 = 11 cm.
The formula to calculate the volume of a sphere is (4/3)πr^3, where r is the radius of the sphere, and π is a mathematical constant that represents the ratio of the circumference of a circle to its diameter (which is approximately 3.14159).
In this case, the question gives us the value of π as 22/7. So to find the volume of the tennis ball, we use the formula as follows:
Volume of tennis ball = (4/3) x (22/7) x (3.5)^3
= (4/3) x (22/7) x (42.875)
= 179.5945 cm^3 (rounded to five decimal places)
Similarly, to find the volume of the football, we use the same formula with a radius of 11 cm and the given value of π as:
Volume of football = (4/3) x (22/7) x (11)^3
= (4/3) x (22/7) x (1331)
= 68040.8947 cm^3 (rounded to five decimal places)
The question asks us to find the difference between the two volumes, which is:
Difference = Volume of football - Volume of tennis ball
= 68040.8947 cm^3 - 179.5945 cm^3
= 67861.3002 cm^3
Since the question asks to round off to the nearest centimetre, we round the difference to the nearest whole number, which is:
Difference = 67861 cm^3.
I hope this explanation clarifies the calculation process.
Please break it down further I am not more than 9 yrs I really need to understand
I'm sorry for not explaining it well enough earlier.
A tennis ball and a football are both round objects known as spheres. The size of a sphere is measured by its diameter which is the length of a straight line passing through its center and touching the surface on either end.
For the tennis ball, we know that its diameter is 7 cm. To find the volume of the tennis ball, we first need to calculate its radius which is half the diameter.
radius of tennis ball = 7/2 = 3.5 cm
Next, we can use the formula to find the volume of a sphere which is:
Volume of sphere = (4/3)πr^3
where r is the radius of the sphere and π is a special number used in mathematics that represents the ratio of the circumference of a circle to its diameter.
The value of π can be approximated to 3.14 or 22/7 (which is a more accurate approximation). The question tells us to use the value of π as 22/7.
Using the radius of the tennis ball, we can calculate its volume as follows:
Volume of tennis ball = (4/3) x (22/7) x (3.5)^3
= 1.33 x 22 x 42.875
= 318.8 cubic centimeters (rounded to one decimal place)
For the football, its diameter is 22 cm. The radius of the football is therefore:
radius of football = 22/2 = 11 cm
Using the same formula, we can calculate the volume of the football as follows:
Volume of football = (4/3) x (22/7) x (11)^3
= 1.33 x 22 x 1331
= 90432 cubic centimeters (rounded to no decimal places)
To find the difference between the two volumes, we simply subtract the volume of the tennis ball from the volume of the football:
Difference = Volume of football - Volume of tennis ball
= 90432 - 318.8
= 90113.2 cubic centimeters (rounded to one decimal place)
Since the question asks us to round off to the nearest centimeter, we round this answer to:
Difference = 90113 cubic centimeters.
I hope that this explanation helps you understand the process better.