David Weber, Talei Kunkel, Rose Harrison and, Fatima Remtulla Solutions for Chapter: 3D Shapes Products, Processes and Solutions, Exercise 21: Practice 5

Find the volume of given shape in ${\mathrm{mm}}^3$.  Round the answer to the nearest tenth.

Find the volume of given shape in ${\mathrm{cm}}^3$.  

Find the volume of given shape in ${\mathrm{mm}}^3$. Round the answer to the nearest tenth. (Use, $\sqrt{3}=1.73$)

Find the volume of given shape.  

Find the missing measurements of the square pyramid.

In the 1990s, hotels on the Las Vegas Strip began a ten-year project to try to attract families with children.The casinos and shows were not enough to bring in this new clientele, so the solution they devised was to build large, themed hotels, complete with rides and attractions. One of these hotels is The Luxor, an Egyptian­ themed resort in the shape of the Great Pyramid of Giza. At night, the brightest beam of light in the world emanates from the top of the pyramid.

With a height of $107 \mathrm{m}$ and a square base with sides of $197 \mathrm{m}$, how much space was available inside the hotel for bedrooms, a convention centre, restaurants and theatres?

Traditional fireplaces are a simple opening in a wall. More modern designs often allow the fireplace to be viewed from two or even three sides. The pyramid fireplace design was created not only to allow viewing from all sides, but also to make it possible to situate the fireplace anywhere in a room.
The volume of air inside the square pyramid fireplace is $114996 {\mathrm{cm}}^3$ and its height is $63 \mathrm{cm}$. Find the length of the side of the base.
 

Traditional fireplaces are a simple opening in a wall. More modern designs often allow the fireplace to be viewed from two or even three sides. The pyramid fireplace design was created not only to allow viewing from all sides, but also to make it possible to situate the fireplace anywhere in a room.
 

What happens to the volume of the fireplace if the sides of the base are doubled in length? Show your working.