0
Add your answer:
Earn +20 pts
What expression gives the surface area of a sphere with the radius r?
Surface area of a sphere: 4*pi*r^2
Why is the volume of a sphere divided by 3?
( The volume of a sphere is (4/3)(pi)r3 ). The short answer: because of calculus. The long answer: This can be seen by using calculus to derive the volume of a sphere from the formula from it's surface area. To do this, we imagine that the sphere is full of infinity thin spheres inside it (all centered at the big sphere's center), and add up the surface areas of all the spheres inside. The formula for the surface area of a sphere is 4(pi)r2. Let's call R the radius of the big sphere we want to find the volume of. To find the volume of this sphere, we add up the surface areas of all the spheres whose radii range from 0 to R. This gives the following formula (where r is the radius of each little sphere): 0R∫ 4(pi)r2dr The 4 and pi can be factored out giving: 4(pi) (0R∫r2dr) Integrating gives: 4(pi) [r3/3]0R This is where the three comes from. Finishing the evaluation of the integral gives: 4(pi)(R3/3 - 03/3) = 4(pi)(R3/3) Which can be rewritten as (4/3)pi(R3) which is the formula for the volume of a sphere.
What is the surface area of a sphere with volume of 140cm?
Volume: 4/3*pi*radius3 = 140 By making the radius the subject of the above gives it a value of 3.221166265 cm Surface area: 4*pi*3.2211662652 = 130.387557 square cm
What is the surface area of a sphere when its volume is 288pi cubic cm showing work?
To find the surface area of a sphere when its volume is 288π cubic cm, we first need to find the radius of the sphere. The formula for the volume of a sphere is V = (4/3)πr^3, where r is the radius. Given that the volume is 288π, we can solve for r: 288π = (4/3)πr^3. Solving for r, we get r = 6 cm. Next, we can find the surface area of the sphere using the formula A = 4πr^2, where r is the radius. Plugging in the radius of 6 cm, we get A = 4π(6)^2 = 144π square cm. Therefore, the surface area of the sphere is 144π square cm.
How does the volume of a cone change if its radius and height are both tripled?
The volume of a cone is pi(r2h)/3 If the radius and height are both tripled, plugging this into the equation gives us pi(3h(3r)2)/3 =pi(3h9r2)/3 =27pi(r2h)/3 which is 27 times the initial volume. Thus if the radius and height of a cone are tripled, the volume multiplies by 27.
Which expression gives the volume of a sphere with a radius 16?
V = 4/3(Pi*r3): A sphere with a radius of 16 units has a volume of ≅17,157.28 cubic units.
Which expression gives the volume of a sphere with radius 17?
(4/3) x (pi) x (17)3
Which expression gives the volume of a sphere with radius 7?
V = 4/3(PI*73) ≅ 1,436.76 units3
What expression gives the volume of a sphere with radius 16?
4/3*Pi*163 = 17,157.28 cubic units
Which expression gives the volume of a sphere with radius 15?
Volume in cubic units = 4/3*pi*153
What the surface are of a sphere with volume of 900in3?
Volume = 4/3*pi*radius3 = 900 cubic inches By making the radius the subject of the above equation gives the sphere a radius of 5.989418137 inches. Surface area = 4*pi*5.9894181372 = 450.7950449 square inches
Which formula gives the volume of a sphere with radius 5?
Volume = 4/3*pi*53 = 523.599 cubic units rounded to 3 decimal places
What is the radius of a sphere if the volume is 523.6cm cubed?
4/3*pi*radius3 = 523.6 Making the radius the subject of the above gives it a value of 5.000003897 or about 5 cm
What the volume of the moon?
The diameter of the moon is about 3474.8 kilometers. The volume of a sphere is equal to 4/3 (pi)(radius cubed). This gives it a volume of approximately 2.1958 E10 cubic kilometers.
What is the volume of a sphere that has a surface area of 49pi square cm?
Well, darling, the surface area of a sphere is given by the formula 4πr², where r is the radius. So, if the surface area is 49π, then the radius squared is 49, making the radius 7 cm. Now, the volume of a sphere is (4/3)πr³, so plugging in a radius of 7 cm gives a volume of 179π cubic cm. Voilà!
What is the volume of a sphere with a radius of 12 cm?
Well, darling, the volume of a sphere is calculated using the formula V = (4/3)πr^3. So, plug in the radius of 12 cm, and you'll find that the volume is approximately 7238.23 cubic centimeters. So, there you have it, sweetie, now go impress someone with your newfound knowledge.
What expression gives the surface area of a sphere with the radius r?
Surface area of a sphere: 4*pi*r^2
