The area of the hexagonal base is 58 square inches.

Mathematics

1 answer:

kenny6666 [7]2 years ago

6 0

Answer:

362.5 in^3

Step-by-step explanation:

V = (face [surface] area)(height)

V = 58(6.25) = 362.5

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Perform the multiplication. Simplify the answers. 2 √30*( √5+ √6+ √10+ √15)

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The simplified expression of $2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15})$ is $10\sqrt{6} + 6\sqrt{20}+ 20\sqrt{3} + 30\sqrt{2}$

The expression is given as:

$2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15})$

Expand the expression

$2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15}) = 2\sqrt{30} \times \sqrt5+ 2\sqrt{30} \times \sqrt6+ 2\sqrt{30} \times \sqrt{10} + 2\sqrt{30} \times \sqrt{15}$

Factor out 2

$2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15}) = 2(\sqrt{30} \times \sqrt5+ \sqrt{30} \times \sqrt6+ \sqrt{30} \times \sqrt{10} + \sqrt{30} \times \sqrt{15})$

Combine the radicals

$2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15}) = 2(\sqrt{150} + \sqrt{180}+ \sqrt{300} + \sqrt{450})$

Expand the expression

$2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15}) = 2(\sqrt{25 \times 6} + \sqrt{9 \times 20}+ \sqrt{100 \times 3} + \sqrt{225\times 2})$

Evaluate the roots

$2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15}) = 2(5\sqrt{6} + 3\sqrt{20}+ 10\sqrt{3} + 15 \sqrt{2})$

Expand

$2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15}) =10\sqrt{6} + 6\sqrt{20}+ 20\sqrt{3} + 30\sqrt{2}$

Hence, the simplified expression of $2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15})$ is $10\sqrt{6} + 6\sqrt{20}+ 20\sqrt{3} + 30\sqrt{2}$

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