A composite geometry is made up of cube and a square pyramid frustum. The slanted side AK stretch a side lengths of 5.62 forming an isosceles triangle. Calculate the volume, surface area and sketch the net of the surface area?
There are some assumptions that we have to make looking at the picture that are not explicitly specified in the problem. See below
 The side length of a cube is
#a=5.84#  The pyramid frustum's top base is a square with a side
#b=3.15#  The pyramid before it was truncated was regular square pyramid
 The plane of truncation (top base of a frustum) is parallel to its bottom base.
 Side edge of the pyramid frustum is defined as
#AK=c=3.15#
Our major task is to define the height of the pyramid frustum
First of all, let's project the top base of the pyramid frustum onto the bottom base of this pyramid. On the bottom base we will see this projection as a square centrally located inside a bigger square  the bottom base. We know dimensions of both squares 
Using a Pythagorean Theorem, we can find a distance from the projection of point
Now, knowing
All the values required in the problem are now easily derived, knowing
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To calculate the volume and surface area of the composite geometry made up of a cube and a square pyramid frustum, and to sketch the net of the surface area, follow these steps:

Calculate the volume of the cube using the formula: ( V_{\text{cube}} = s^3 ), where ( s ) is the length of the side of the cube.

Calculate the volume of the square pyramid frustum. The volume of a square pyramid frustum is given by the formula: [ V_{\text{frustum}} = \frac{h}{3} \cdot (A_1 + A_2 + \sqrt{A_1 \cdot A_2}) ] Where:
 ( h ) is the height of the frustum,
 ( A_1 ) and ( A_2 ) are the areas of the two parallel square bases.

Add the volumes of the cube and the frustum to find the total volume of the composite geometry.

Calculate the total surface area. It includes the surface area of the cube and the lateral surface area of the frustum.
 Surface area of the cube: ( SA_{\text{cube}} = 6s^2 )
 Lateral surface area of the frustum: ( SA_{\text{frustum}} = \frac{1}{2} \cdot (P_1 + P_2) \cdot l ) Where:
 ( P_1 ) and ( P_2 ) are the perimeters of the top and bottom bases,
 ( l ) is the slant height of the frustum.

Add the surface areas of the cube and the frustum to find the total surface area of the composite geometry.

Sketch the net of the surface area by drawing the unfolded version of the composite geometry, showing all the faces.
Calculate the values using the given dimensions and formulas to find the volume, surface area, and sketch the net of the surface area.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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