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Works through multiple example problems, solving for radius or total area using given radius, diameter, or Earth’s northern hemisphere dimensions, with step-by-step calculations and final area or radius 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is the formula for the total surface area of a sphere?","Question",{"text":63,"@type":64},"The total surface area of a sphere is Asphere = 4πr², where r is the radius.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How do you calculate the total surface area of a hemisphere?",{"text":68,"@type":64},"Find the top area using Atop = πr² (circle area), find the bottom area as half of the sphere area, then add them: Atotal = Atop + Ahemisphere.",{"name":70,"@type":61,"acceptedAnswer":71},"What should you do if the problem gives surface area and asks for the radius?",{"text":72,"@type":64},"Use the relevant equation (for a sphere, Asphere = 4πr²), substitute the given area, and solve for r or r² before taking the square root if 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a Sphere  \nRemember that a sphere looks like this:  \nThe formula for the total surface area of a sphere is:  \nAsphere = ( 4 ) ( π ) ( r 2 )  \nWhere “r” is the radius.  \nLet’s find the total surface area of a sphere.  \nCalculate the total area of the following sphere, given the information below.  \nWe know that the radius r = 7 m.  \nUse Asphere = ( 4 ) ( π ) ( r 2 )= ( 4 ) ( π ) ( 7 m )2 = 615.75 m2  \n615.75 m2 is the total area.  \nSometimes we will know the total surface area of a sphere, and we will be asked to find its radius.  \nCalculate the radius of the following sphere, given the information below.  \nAsphere = 1809.56 m2 Asphere = ( 4 ) ( π ) ( r 2 )  \n1809.56 m2 = ( 4 ) ( π ) ( r 2 )  \n1894~~)~~.5~~( ~~6π2 = r 2  \n1809.56 m2 = r 2 12.57  \n144 m2 = r 2  \n 144 m2 = r  \nr =12 m  \nFinally, we need to know how to calculate the total surface area of a hemisphere.  \n1  \nThis resource can be used for FREE by any teacher / student with an active Math Help Services account  \nRemember that a hemisphere looks like this:  \nTo calculate the area of the top, we will use the equation for the area of a circle:  \nAtop = ( π ) ( r 2 )  \nTo calculate the area of the bottom, we will use the equation for the area of a sphere and divide by 2:  \n( ) ( ) ( )  \n2 r  \n4 π A hemisphere =  \n2  \nTo calculate the total surface area, we simply add the two above results together.  \nA total = Atop + Ahemisphere  \nLet’s try an example of this.  \nthe total surface area of the  \nhemisphere, given the information  \nCalculate following below.  \nWe know that r = 5 cm  \nUse Atop = ( π ) ( r 2 )= ( π ) ( 5 cm )2 = 78.54 cm2  \nUse  ( ) ( ) ( )  \nA hemisphere  \n4  \n=  \nπ  \n2  \n2 r  \n( ) ( ) ( )  \n2 = 4 π 5 cm   \n2  \n=  314.16 cm2  \n2 = 157.08 cm2  \nUse Atotal = Atop + Ahemisphere = 78.54 cm2 +157.08 cm2 = 235.62 cm2  \n235.62 cm2 is the total surface area.  \nWe are ready to try more challenging questions.  \n2  \nThis resource can be used for FREE by any teacher / student with an active Math Help Services account  \nExample  \n1. Calculate the total area of the following sphere, given the information below.  \nRadius = 2 cm  \nStep 1: State the information that you know  \nr = 2 cm  \nStep 2: Use the total surface area equation for spheres  \nAsphere = ( 4 ) ( π ) ( r 2 )= ( 4 ) ( π ) ( 2 cm )2 = 50.27 cm2  \n50.27 cm2 is the total surface area.  \n2. Calculate the total area of the following sphere, given the information below.  \nDiameter = 5 cm  \nStep 1: State the information that you know  \nd = 5 cm r = 2.5 cm  \nStep 2: Use the total surface area equation for spheres  \nA sphere = ( 4 ) ( π ) ( r 2 )= ( 4 ) ( π ) ( 2.5 cm )2 = 78.54 cm 2  \n78.54 cm2 is the total surface area.  \n3  \nThis resource can be used for FREE by any teacher / student with an active Math Help Services account  \n3. Calculate the total area of the following hemisphere, given the information below.  \nRadius = 3 cm  \nStep 1: State the information that you know  \nr = 3 cm  \nStep 2: Use the area of the top (circle)  \nAtop = ( π ) ( r 2 )= ( π ) ( 3 cm )2 = 28.27 cm2  \nStep 3: Calculate the area of the bottom (hemisphere)  \nA hemisphere = ~~ ~~(~~ ~~4~~ ~~)~~ ~~(~~ ~~π2)~~ ~~(~~ ~~r~~ ~~2~~ ~~)=  ( 4 ) ( π ) ( 3 cm )2  \n2  \n=  113.1 cm2  \n2  \n= 56.55 cm2  \nStep 4: Calculate the total surface area  \nAtotal = Atop + Ahemisphere = 28.27 cm2 + 56.55 cm2 = 84.82 cm2  \n84.82 cm2 is the total surface area.  \n4. Calculate the radius of the following hemisphere, given the information below.  \n Asphere = 1520.53 cm2  \nStep 1: State the information that you know  \nAsphere = 1520.53 cm2  \nStep 2: Use the total surface area equation for spheres to find the radius  \nAsphere = ( 4 ) ( π ) ( r 2 )  \n1520.53 cm2 = ( 4 ) ( π ) ( r 2 ) 152~~(~~04.~~(~~3πc~~)~~m2 = r 2  \n1520.53 cm2 = r 2 12.57  \nr 2 = 121 cm2  \nr = 121 cm2  \nr = 11 cm  \nr = 11 is the radius  \n4  \nThis resource can be used for FREE by any","cbCaiqICpgn9PWMr","https://ap.wps.com/l/cbCaiqICpgn9PWMr","pdf",352597,"English","# The surface area of a sphere\n## Total surface area formula and example\n## Solving for radius from given area\n# The surface area of a hemisphere\n## Top and bottom area method\n## Total hemisphere surface area example\n# Practice problems\n## Sphere examples\n## Hemisphere examples\n## Earth northern hemisphere problem","[{\"question\":\"What is the formula for the total surface area of a sphere?\",\"answer\":\"The total surface area of a sphere is Asphere = 4πr², where r is the radius.\"},{\"question\":\"How do you calculate the total surface area of a hemisphere?\",\"answer\":\"Find the top area using Atop = πr² (circle area), find the bottom area as half of the sphere area, then add them: Atotal = Atop + Ahemisphere.\"},{\"question\":\"What should you do if the problem gives surface area and asks for the radius?\",\"answer\":\"Use the relevant equation (for a sphere, Asphere = 4πr²), substitute the given area, and solve for r or r² before taking the square root if needed.\"}]","The Surface Area of a Sphere and Hemisphere - Free Math Practice | PDF",13]