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SCORPION-xisa [38]
3 years ago
8

A sold sphere has volume 42pie. Find the radius of the sphere

Mathematics
1 answer:
Over [174]3 years ago
7 0

Answer:

The Radius of sphere is 3.15 unit  

Step-by-step explanation:

Given as,

Volume of Sphere = 42 \pi    unit³

From the Volume of Sphere = \frac{4}{3} \pi r³

Where r is the radius of Sphere

So , 42 \pi  = \frac{4}{3} \pi r³

Or,  42  = \frac{4}{3} r³

Or ,  r³ = (\frac{42 \times 3}{4})

Or,   r³ = 31.5

Or, Radius = \sqrt[3]{31.5} = 3.15 unit

Hence the Radius of sphere is 3.15 unit   Answer

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Given:

Length of each edge a=8cm

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<u>Step by Step Explanation: </u>

Solution;

Formula for calculating slant height is given as

Slant height=\sqrt{\frac{2}{3}} a

Where a= length of each edge

Slant height=\sqrt{\frac{2}{3}} \times 8

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Similarly formula used for calculating volume is given as

Volume of the tetrahedron=\frac{a^{3}}{6 \sqrt{2}}

Substitute the value of a in above equation we get

Volume=\frac{8^{5}}{6 \sqrt{2}}

            =\frac{512}{6 \sqrt{2}}

            =\frac{512}{6 \times 1.414}

Volume=512 / 8.484=60.35\mathrm{cm}^{3}

Result:

Thus the slant height and volume of tetrahedron are 6.53cm and 60.35\mathrm{cm}^{3}

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