Solid geometry › Cylinders, cones and spheres

Changing cylinder dimensions

Solve the first problem 17 problems

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1. Small pipes matching one large pipe ●○○○○ 10 ptsA pipe with inside diameter $10''$ is to carry water from a reservoir to a small town in an arid land. Neglecting the friction and turbulence of the water against the inside of the pipes, what is the minimum number of $2''$-inside-diameter pipes of the same length needed to carry the same volume of water to the arid town?
2. Tin can versus cylinder capacity ●○○○○ 10 ptsA tin can has a rectangular base of length $5\ \mathrm{cm}$ and width $4\ \mathrm{cm}$, and height $15\ \mathrm{cm}$. A plastic cylinder has a circular base of diameter $7\ \mathrm{cm}$ and height $10\ \mathrm{cm}$. Use $\pi \approx \frac{22}{7}$. By how many $\mathrm{cm}^3$ is the capacity of the plastic cylinder greater than the capacity of the tin can?
3. Extra capacity of a plastic cylinder ●○○○○ 10 ptsA tin can has a rectangular base of length 5 cm and width 4 cm, and height 15 cm. A plastic cylinder has a circular base of diameter 7 cm and height 10 cm. By how many cm³ is the capacity of the larger container greater than that of the smaller one? Use $\pi \approx \frac{22}{7}$.
4. Volumes of two paper tubes ●●○○○ 20 ptsAmy and Belinda each roll a sheet of 6-inch by 8-inch paper to form a cylindrical tube. Amy tapes the two 8-inch sides together without overlap. Belinda tapes the two 6-inch sides together without overlap. What is $\pi$ times the positive difference of the volumes of the two tubes?
5. Radius of the wider can ●●○○○ 20 ptsTwo cylindrical cans have the same volume. The height of one can is triple the height of the other. If the radius of the narrower can is 12 units, find the radius of the wider can in units. Round to two decimal places.
6. Height of a pile of three pipes ●●○○○ 20 ptsThree identical cylindrical pipes, each with diameter $10\text{ cm}$, are stacked so that each pipe touches the other two: two lie side by side on the ground and the third rests on top of them, touching both. Let $h$ be the height of this pile, from the ground to the top of the highest pipe. Find $h$ in cm. Round to two decimal places.

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