−9+1/4(8n+16)=1/4(20n+4) help pls

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cesar2679

13.11.2022

Mathematics

The volume of pyramid B is 64 times the volume of pyramid A.

Step-by-step explanation:

Given:

Two square pyramids A and B.

Side Length of A, s_A = 12 inches

Height of A, h_A = 8 inches

Side Length of B, s_B = 48 inches

Height of B, h_B = 32 inches

To find:

How many times bigger is the volume of pyramid B than pyramid A?

V_B is how many times bigger than V_A ?

Solution:

First of all, let us have a look at the formula for volume of a pyramid:

$V=\dfrac{1}{3} \times \text{Area of Base} \times \text{Height}$

Here, base is square, so:

$V=\dfrac{1}{3} \times s^2 \times h$

Volume of pyramid A:

$V_A=\dfrac{1}{3} \times s_A^2 \times h_A$

$\Rightarrow V_A=\dfrac{1}{3} \times 12^2 \times 8 = 384\ inch^3$

Volume of pyramid B:

$V_B=\dfrac{1}{3} \times s_B^2 \times h_B$

$\Rightarrow V_B=\dfrac{1}{3} \times 48^2 \times 32 \\\Rightarrow V_B=\dfrac{1}{3} \times 12^2 \times 8 \times 4^2 \times 4\\\Rightarrow V_B=\dfrac{1}{3} \times 12^2 \times 8 \times 64\\\Rightarrow V_B= 24576\ inch^3 = 384\times 64\ inch^3\\\Rightarrow V_B = V_A\times 64\ inch^3$

The volume of pyramid B is 64 times the volume of pyramid A.

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