Q: What expression gives the surface area of a sphere with the radius r?

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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

4/3 pie(7exponent3)

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

( 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.

There are 2 types of surface areas;Total Surface Area(TSA) which gives the complete surface area of the solidLateral/Curved Surface Area(LSA/CSA) which gives the surface area of the solid excluding the top and base areas. (eg, area of 4 walls of a room or area of the canvas required for a conical tent)For a Cube with a side a:LSA: 4x(square of a side) or 4a2TSA: 6a2For a cuboid with length l,breadth b, height h:LSA: 2h(l+b)TSA: 2(lb+bh+hl)For a cylinder with radius of base r and heigth h:LSA: 2Ï€rhTSA: Ï€r2hFor a cone with radius r, height h, slant height l:LSA: Ï€rlTSA: Ï€r(l+r)For a sphere with radius r:LSA=TSA=4Ï€r2For a hemisphere with radius r:LSA: 2Ï€r2TSA: 3Ï€r2Sorry, I dont know any more than this!!

Related questions

Area = 4*pi*r^2

(4/3) x (pi) x (17)3

V = 4/3(PI*73) ≅ 1,436.76 units3

4/3*Pi*163 = 17,157.28 cubic units

V = 4/3(Pi*r3): A sphere with a radius of 16 units has a volume of ≅17,157.28 cubic units.

If you mean 4*pi*r^2 then it is the formula for finding the surface area of a sphere

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

Volume in cubic units = 4/3*pi*153

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

Surface area: 4*pi*radius2 = 803.84 Making the radius the subject of the above gives it a value of 7.9979719132 or about 8 units in length. Check: 4*pi*7.99797191322 = 803.84 square units

4/3 pie(7exponent3)

The surface area is 4 pi r 2. Radius is 7.6cm. This gives you 725.47cm2 rounded up in the hundreds