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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
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.
What is the surface area of a sphere with a circumference of 41 inches?
Diameter: 41/pi = 13 inches rounded to a whole number Radius: 13/2 = 6.5 inches Surface area of the sphere: 4*pi*6.5 squared = 530.929 square inches to three decimal places
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 expression gives the surface area of a sphere with the radius r?
Surface area of a sphere: 4*pi*r^2
What is half the volume of a sphere that has a diameter of 6?
The formula for the volume of the sphere is:v= volumer= radiusTo find the radius, you divide the diameter by 2 since the diameter is twice the radius.6/2 = 3 = radiusThen you just plug it in the formulaV= 4/3 pi 33V= 4/3 pi 9V= 12 piV= 37.6991118Now, to find half the volume, you need to divide 37.6991118 by 2 which gives you 18.8495559
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.
