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ehidna [41]
3 years ago
15

The Volume of a sphare is 28/3 times the surface area calculate The surface area and the Volume of the sphere, correct to the ne

arest whole number.​
Mathematics
1 answer:
Aloiza [94]3 years ago
3 0

Given:

Volume of a sphere is \dfrac{28}{3} times the surface area.

To find:

The surface area and the volume of the sphere.

Solution:

Volume of a sphere:

V=\dfrac{4}{3}\pi r^3              ...(i)

Surface area of a sphere:

A=4\pi r^2                      ...(ii)

Where, r is the radius of the sphere.

Volume of a sphere is \dfrac{28}{3} times the surface area.

V=\dfrac{28}{3}\times A

\dfrac{4}{3}\pi r^3=\dfrac{28}{3}\times 4\pi r^2

Multiply both sides by 3.

4\pi r^3=112\pi r^2

\dfrac{\pi r^3}{\pi r^2}=\dfrac{112}{4}

r=28

Using (i), the volume of the sphere is:

V=\dfrac{4}{3}\times \dfrac{22}{7}\times (28)^3

V\approx 91989

Using (ii), the surface area of the sphere is:

A=4\times \dfrac{22}{7}\times (28)^2

A=9856

Therefore, the surface area of the sphere is 9856 sq. units and the volume of the sphere is 91989 cubic units.

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