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A sphere has a surface area of 616 cm2. What is its radius? (Use ╧А=22/7)
5
7
14
10.5
7
Since the formula involves 4├Ч722тАЛ├Чr2, look for a radius r such that r2 is divisible by 7. For r=7, r2=49, which cancels the 7 in the denominator perfectly.
Surface area of the sphere S = 616 cm┬▓ and the value of ╧А is 22/7.
S=4╧Аr2
Since the formula involves 4├Ч722тАЛ├Чr2, look for a radius r such that r2 is divisible by 7. For r=7, r2=49, which cancels the 7 in the denominator perfectly.
Students often confuse the surface area of a sphere 4╧Аr2 with the curved surface area of a hemisphere 2╧Аr2 or the area of a circle ╧Аr2.
State the surface area formula
The surface area S of a sphere with radius r is given by the formula:
S=4╧Аr2
Substitute the known values
Substitute S=616 and ╧А=722тАЛ into the equation:
616=4├Ч722тАЛ├Чr2
Solve for r┬▓
Isolate r2 by multiplying both sides by 7 and dividing by 4├Ч22 (88):
r2=88616├Ч7тАЛ=7├Ч7=49
Calculate the final radius
Taking the square root of 49 gives the radius:
r=49тАЛ=7
B is correct because the calculation of the radius r=88616├Ч7тАЛтАЛ results in 7 cm.
This concept is fundamental for volume problems. Remember that if surface area is given, always find the radius r first to calculate the volume using V=34тАЛ╧Аr3.