A certain square pyramid has a volume of $100 cm^3$ . A similar but smaller pyramid has a surface area equal to one fifth of the larger. What is the volume of the smaller pyramid?

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A certain square pyramid has a volume of $100 cm^3$ . A similar but smaller pyramid has a surface area equal to one fifth of the larger. What is the volume of the smaller pyramid?

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Answer 1 · 2018-02-13T21:40:12

$"volume "=4sqrt5~~8.944" cubic cm"$

Explanation:

$"consider 2 similar figures then"$

$"linear ratios "=a:b$

$"area ratios "=a^2:b^2$

$"volume ratios "=a^3:b^3$

$"here "a^2:b^2=1:5$

$rArra:b=sqrt1:sqrt5=1:sqrt5$

$rArra^3:b^3=1^3:(sqrt5)^3=1:5sqrt5$

$rArr"volume of smaller pyramid "=100/(5sqrt5)$

$rArr"volume "=20/sqrt5xxsqrt5/sqrt5=4sqrt5" cubic cm"$

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A certain square pyramid has a volume of $100 cm^3$ . A similar but smaller pyramid has a surface area equal to one fifth of the larger. What is the volume of the smaller pyramid?

1 Answer

Explanation:

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Science

Math

Humanities

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A certain square pyramid has a volume of 100 cm^3100 cm^3. A similar but smaller pyramid has a surface area equal to one fifth of the larger. What is the volume of the smaller pyramid?

1 Answer

Explanation:

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A certain square pyramid has a volume of $100 cm^3$ . A similar but smaller pyramid has a surface area equal to one fifth of the larger. What is the volume of the smaller pyramid?