Question

PLEASE HURRY!! The ratio of the volumes of two geometrically similar pyramids is 1 : 8. If the height of the larger pyramid is 24 inches, what is the height of the smaller pyramid?

a = 3 inches
b = 6 inches
c = 12 inches
d = 17 inches

Answer 1

Answer:

Answer C.12

Step-by-step explanation:

v/V=(h/H)^3

1/8=(h/24)^3

1/8=h^3/24^3

1/8=h^3/13824

8h^3=13824

H=1728√3

h= \sqrt[3]{1728}

h=12 cm

Answer 2

the height of the smaller pyramid is 12 inches.

What is a triangular pyramid?

A triangular pyramid is a 3D geometric shape in which all the three lateral faces are triangles with a common vertex. If all the three triangular faces are equilateral, then such a pyramid is called a tetrahedron.

For the given situation,

The ratio of the volumes of two geometrically similar pyramids = 1:8

The height of the larger pyramid = 24 inches.

Let the volume of smaller pyramid be v1 and larger pyramid be v2.

Let the height of smaller pyramid be h1 and larger pyramid be h2.

The relation between the volume of pyramid and height is given as

$v=\frac{1}{3} (base area)(height)$

Let us consider the triangle to be equilateral triangle. So all the sides are equal.

We know that, Base area = $a^{2}$ and $a=h$

The volume becomes $v=\frac{1}{3} h^{3}$

The ratio becomes,

⇒ $\frac{v1}{v2} =\frac{h1^{3} }{h2^{3}}$

⇒ $\frac{1}{8} =\frac{h1^{3} }{24^{3}}$

⇒ $h1^{3}=\frac{24^{3} }{8}$

⇒ $h1^{3}=\frac{13824 }{8}$

⇒ $h1^{3}=1728$

⇒ $h1=\sqrt[3]{1728}$

⇒ $h1=12$

Hence we can conclude that the height of the smaller pyramid is           12 inches.

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