David Weber, Talei Kunkel, Rose Harrison and, Fatima Remtulla Solutions for Chapter: 3D Shapes Products, Processes and Solutions, Exercise 35: Unit review

The Morning Glory cloud formation occurs very predictably on the north coast of Australia. Although its causes are not known precisely, it forms mostly in October over the Gulf of Carpentaria during a process when sea breezes from the west meet breezes from the east. To study such phenomena, scientists use a tool called a radiosonde, attached to a weather balloon (which is spherical!). These cylindrical cloud formations can be $1000$ km long with a radius of $150$ m. Moving at speeds up to $60$ km/h, there is a lot of cloud moving overhead. If the cloud formation were only half as long, by what factor would that change the surface area? Justify your answer with calculations. 

The Morning Glory cloud formation occurs very predictably on the north coast of Australia. Although its causes are not known precisely, it forms mostly in October over the Gulf of Carpentaria during a process when sea breezes from the west meet breezes from the east. To study such phenomena, scientists use a tool called a radiosonde, attached to a weather balloon (which is spherical!). These cylindrical cloud formations can be $1000$ km long with a radius of $150$ m. Moving at speeds up to $60$ km/h, there is a lot of cloud moving overhead. If the cloud formation had only half the radius, by what factor would that change the surface area? Justify your answer with calculations.

A common product found in many restaurants and kitchens is the pepper grinder. It allows users to grind their own pepper, keeping it as fresh as possible until used. Pepper grinders can come in a wide range of shapes and sizes. One product is in the shape of a cylinder with a height of $14$ cm and a radius of $5$ cm. Another is in shape of a ball (sphere). If the radius of a ball pepper grinder if it has to contain the same volume of pepper as the cylinder rounded to nearest tenths is $R$ cm then find $R$.

Access to clean water is a problem in many developing countries, especially as clean water sources are often located far away from the people who need the water. The Q Drum water transporter was developed to solve this problem. Its design allows it to transport a large volume of water over long distances simply by rolling the drum. This means that anyone can use the device, including children. The Q Drum holds $50000 {\text{cm}}^3$ of water. Its height is $36$ cm and the diameter of the base is $50$ cm. If the radius of the inner hole through the centre of the drum rounded to the nearest tenths is $r$ cm then find $r$.

The traditional igloo, with its approximately hemispherical dome, is traditionally built by Canadian Inuit and the people of Greenland. It is made of compacted snow, which is a poor conductor of heat, so any heat generated inside the structure will stay inside. If the radius inside an igloo is $1.8$ m, and the volume of air contained inside rounded nearest to tenths is $V {\text{m}}^3$ then find $V$. (Disregard the entranceway in your answers to this question. Just find the volume and surface area of the hemisphere and take $\pi =22/7$)

The traditional igloo, with its approximately hemispherical dome, is traditionally built by Canadian Inuit and the people of Greenland. It is made of compacted snow, which is a poor conductor of heat, so any heat generated inside the structure will stay inside. If the thickness of the walls of compacted snow is $0.5$ m and the inner radius of the igloo is  $0.8$ m, if the surface area of the outside of the igloo rounded to the nearest tenths is $S {\text{m}}^2$ then find $S$. (Take $\pi =22/7$)

The two-piece hard capsule, patented in $1847$, was designed both to ensure the correct dosage of a medication and to make the medicine easy to swallow, without having to taste the medicine. The pharmaceutical manufacturer fills the hollow gelatin capsule with medicines such as antibiotics. Capsules come in many sizes, but a common one has a total length of $11$ mm and a diameter of $5$ mm. If the volume of medicine that a capsule of this size can hold rounded off to tenths place is $V {\text{mm}}^3$ then find $V$. (Take $\pi =22/7$)

The two-piece hard capsule, patented in $1847$, was designed both to ensure the correct dosage of a medication and to make the medicine easy to swallow, without having to taste the medicine. The pharmaceutical manufacturer fills the hollow gelatin capsule with medicines such as antibiotics. Capsules come in many sizes, but a common one has a total length of $11$ mm and a diameter of $5$ mm. If the amount of gelatin needed to produce one capsule rounded off to tenths place is $S {\text{mm}}^2$ then find $S$. (Take $\pi =22/7$)