Rose Harrison and Clara Huizink Solutions for Exercise 16: Practice 3

The surface area of a sphere varies directly as the square of its radius. The surface area of a sphere with radius $5 \mathrm{cm}$ is $100\pi {\mathrm{cm}}^2$. Find the surface area of a sphere with radius $2 \mathrm{cm}$.

The surface area of a sphere varies directly as the square of its radius. The surface area of a sphere with radius $5 \mathrm{cm}$ is $100\pi {\mathrm{cm}}^2$. From the information above, or otherwise, write down the formula for the surface area of a sphere.

The surface area of a sphere varies directly as the square of its radius. The surface area of a sphere with radius $5 \mathrm{cm}$ is $100\pi {\mathrm{cm}}^2$. State what happens to the surface area of a sphere when the radius is enlarged by a factor of $5$.

The surface area of a sphere varies directly as the square of its radius. The surface area of a sphere with radius $5 \mathrm{cm}$ is $100\pi {\mathrm{cm}}^2$. Determine the effect on the radius of halving the surface area of a sphere.

The weight of an object in Newtons ($N$) varies inversely with the square of its distance in $km$ from the center of the Earth. The radius of the Earth is approximately $3670\mathrm{km}$. A certain astronaut weighs $850N$ at the surface of the Earth. Find the weight of the same astronaut when she's on the International Space Station, which orbits at an average of $400 km$ from the surface of the earth.

The rings of Saturn have been found to be made up of particles of a variety of sizes. Amazingly, the abundance is inversely proportional to the cube of the size of the particle. If a $2$-meter size particle has an abundance of $10\%$ determine the abundance of a $3$-meter size particle, to the nearest tenth of a percent.

Under the right conditions, pyrite (often called fool's gold) will form in the shape of a perfect cube. The cost of an ounce of this pyrite varies directly with its volume. If a cube with side length of $5 \mathrm{cm}$ costs $\$24$ per ounce, determine the length of the side of a piece of pyrite that costs $\$40$ per ounce.

The use of low-flow shower heads has become an easy way to reduce our water consumption. Regular shower heads use $30$ liters of water per minute while low-flow shower heads may use only $8$ liters per minute. This volume of water is directly proportional to the square of the radius of the pipe in the shower head. If a regular shower head has a pipe with a radius of $5 \mathrm{cm}$ what should be the radius of a pipe in a low-flow shower head?