Volume of a hollow sphere is 11352/7 cm³. If the outer diameter is 16 cm , find the inner radius and outer surface area of the sphere .
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Answered by
33
since, volume of hollow sphere =4/3×pi×(R^3-r^3)
=4/3×22/7×(8^3-r^3)=11352/7
=88/21×(512-r^3)=11352/7
=512-r^3=11352/7×21/88
=512-r^3=387
=-r^3=387-512=-125
so,r^3=125
therefore r=5.
Now, outer surface area=4×pi×r^2
=4×22/7×8^2
=(88/7×64)cm^2
=5632/7 cm^2
=4/3×22/7×(8^3-r^3)=11352/7
=88/21×(512-r^3)=11352/7
=512-r^3=11352/7×21/88
=512-r^3=387
=-r^3=387-512=-125
so,r^3=125
therefore r=5.
Now, outer surface area=4×pi×r^2
=4×22/7×8^2
=(88/7×64)cm^2
=5632/7 cm^2
Answered by
5
Answer:
volume of a hollow sphere= 11352/7
4/3π(R³-r³)= 11352/7
4/3×22/7(8³-r³)=11352/7
88/21×512-r³=11352/7
512-r³=11352/7×21/88
512-r³=387
-r³=387-512
-r³=-125
r³=125
r=5
outer surface area =4πr²
5×22/7×8²
88/7×64=5632/7cm²
answer is 5632/7 cm²
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