David Weber, Talei Kunkel, Rose Harrison and, Fatima Remtulla Solutions for Chapter: 3D Shapes Products, Processes and Solutions, Exercise 23: Practice 6

Find the volume and surface area of the following figures. Round your answer to the nearest tenth.

Find the volume and surface area of the following figure. Round your answer to the nearest tenth.

Find the volume and surface area of the following figure. Round your answer to the nearest tenth.

Dice play an important part of role-playing games. Because not all scenarios have six options, it was necessary to make dice with different numbers of sides. You can now get dice with $4$, $6$, $8$, $12$ and even $20$ sides! A four-sided die (abbreviated d$4$) is a triangular pyramid, all of whose faces are equilateral triangles. If the apothem of any side of the pyramid is $18$ mm and the length of the sides of the triangle is $10.4$ mm, If the surface area of the dice is $S {\text{mm}}^2$ then find $S$. 

Dice play an important part of role-playing games. Because not all scenarios have six options, it was necessary to make dice with different numbers of sides. You can now get dice with $4$, $6$, $8$, $12$ and even $20$ sides! A four-sided die (abbreviated d$4$) is a triangular pyramid, all of whose faces are equilateral triangles. If the apothem of any side of the pyramid is $18$ mm and the length of the sides of the triangle is $10.4$ mm, Is a d$4$ fair? Explain.

Many of the collections at the Louvre can be accessed underground via hallways and corridors. The designer of the Louvre Pyramid wanted to use as much natural light as possible to illuminate these subterranean passageways. In addition to the main Louvre Pyramid, there are also three smaller ones that serve as skylights that let in light where three main hallways meet. These, too, are square pyramids and are made of glass (with the exception of the base). If each of the three small pyramids is covered in a total of $79 {\mathrm{m}}^2$ of glass, and the apothem of each of the triangular sides measures $6.75$ m. If the side length of the base of each small pyramid rounded off to the nearest hundredths is $a$ m then find $a$? 

Using technology is often seen as an individual activity. One company hopes to solve this problem by promoting group interaction when using technology. They have developed a pyramid-shaped holographic display that sits on a tabletop. Users can interact with objects inside the pyramid using their smartphone or tablet. The device is a square pyramid with sides measuring $45$ cm. The height of the pyramid is $23$ cm. If the surface area of the entire device nearest to tenths is $S {\mathrm{cm}}^2$ then find $S$.

Using technology is often seen as an individual activity. One company hopes to solve this problem by promoting group interaction when using technology. They have developed a pyramid-shaped holographic display that sits on a tabletop. Users can interact with objects inside the pyramid using their smartphone or tablet. The device is a square pyramid with sides measuring $45$ cm. The height of the pyramid is $23$ cm. If the percentage of the total surface area that is available for viewing is $P \%$ (is rounded off to the nearest tenths) then find $P$.