Question

First drop down answer choices A. 5.8B. 7.8C. 4 D. 5 Second drop down answer choices A. 48 B. 60 C. 96Third drop down answer choices A. 48 B. 60 C. 96Fourth drop down answer choices A. 2B. 1/2 C. 1

Answer 1

Given the figure of a square pyramid

As shown, the base is a square with a side length = 6

And the slant height = 5

We will find the following:

a) The height of the pyramid

We will use the Pythagorean theorem to find the height of the pyramid

As shown in the following figure:

The height = h

The value of x = 6/2 = 3

So, there is a right angle triangle with legs of 3 and (h) and the

hypotenuse = 5

So, we will find (h) as follows:

$\begin{gathered} h^2+3^2=5^2 \\ h^2=5^2-3^2=25-9=16 \\ h=\sqrt[]{16}=4 \end{gathered}$

So, the answer will be option C. 4

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b) The volume of the pyramid

The volume of the pyramid will be calculated using the following formula:

$V=\frac{1}{3}\cdot B\cdot h$

Where B is the area of the base, (h) is the height of the pyramid

So, the volume will be as follows:

$V=\frac{1}{3}\cdot6^2\cdot4=48$

So, the answer will be option A. 48

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c) The surface area of the pyramid

The surface area = the area of the base + area of the triangular sides

The triangular sides have the same equal base = 6

And the same height = 5

So, the surface area =

$6^2+4\cdot(\frac{1}{2}\cdot6\cdot5)=36+2\cdot6\cdot5=96$

So, the answer will be option C. 96

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d) The horizontal cross-section (that is not the base) is a dilation of the base using the apex as a center of dilation

So, the dilation factor will be less than 1 as the length decrease as we goes to the apex

so, the answer will be option B. 1/2