Question

The first attempt of the basic design of a new toy io shown

Answer 1

We will have the following:

We will determine the total surface area of the toy as follows:

We can see that the total surface area is given by the surface area of the rectangular prism plust the area of the regular cylinder minus the area of one of the circular faces of the cyinder, that is:

Rectangular prism:

$A_p=2((24\cdot8)+(8\cdot10)+(24\cdot10))\Rightarrow A_p=2(192+80+240)$$\Rightarrow A_p=2(512)\Rightarrow A_p=1024$

Cylinder minus one circular face:

$A_c=(2\pi(3)\cdot16)+(\pi(3)^2)\Rightarrow A_c=96\pi+9\pi$$\Rightarrow A_c=105\pi$

Finally, the total surface area is given by:

$A_T=A_p+A_c\Rightarrow A_T=1024+105\pi$$\Rightarrow A_T\approx1354$

So, the total surface area is approximately 1354 in^2.