The mirrored ball was created in order to reflect light around the inside of night clubs. The sphere is covered with small mirrors and rotates while a light shines onto it. The small mirrors reflect light into different parts of the club as the ball turns. Used as early as the $1920$s, the balls gained wide popularity in $1970$s disco clubs and are often referred to as "disco balls". If the typical disco ball has a radius of $42$ cm, what surface area can be covered with mirrors? Round your answer to the nearest hundredth. 

Which would be more effective at heating up a liquid, $10$ Throbber heating balls, each with a radius of $6$ cm or $5$ heating balls each with a radius of $12$ cm? Show your working and justify your answer.

In $1963$, Aquilino Cosani, an Italian manufacturer of plastics, perfected a process to produce puncture-resistant plastic balls. At first, they were used with infants and newborns, but they have since been used for physical therapy, exercise and even as an alternative to a regular desk chair. Cosani's exercise balls come in a wide range of sizes, from $22$ cm in diameter to $85$ cm in diameter. By what factor does the surface area of an exercise ball increase when its radius is doubled? Use mathematics to justify your answer. 

In $1963$, Aquilino Cosani, an Italian manufacturer of plastics, perfected a process to produce puncture-resistant plastic balls. At first, they were used with infants and newborns, but they have since been used for physical therapy, exercise and even as an alternative to a regular desk chair. Cosani's exercise balls come in a wide range of sizes, from $22$ cm in diameter to $85$ cm in diameter. By what factor does the surface area of an exercise ball increase when its radius is tripled?

In 1963, Aquilino Cosani, an Italian manufacturer of plastics, perfected a process to produce puncture-resistant plastic balls. At first, they were used with infants and newborns, but they have since been used for physical therapy, exercise and even as an alternative to a regular desk chair. Cosani's exercise balls come in a wide range of sizes, from 22 cm in diameter to 85 cm in diameter. Generalize the relationship between an increase in radius and its effect on the surface area of a sphere.

Find the volume and surface area of the following sphere. Round your answers to the nearest tenth $(\text{Take} \pi =3.14)$.

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

Find the volume and surface area of the following shape. Round your answer to the nearest tenth. $\left(\text{Take} \mathrm{\pi }=3.14\right)$

Find the volume and surface area of the following shape. Round your answer to the nearest tenth. $\left(\text{Take} \mathrm{\pi }=3.14\right)$