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10 problems match “cuboid”. Clear

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1. 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?
2. People in a cinema hall ●○○○○ 10 ptsThe dimensions of a cinema hall are 100 m, 50 m and 18 m. Each person requires 150 m³ of air. How many people can sit in the hall?
3. Persons accommodated in a hall ●○○○○ 10 ptsA hall is 16 m long, 14 m wide and 5 m high. Calculate the number of persons that can be accommodated in the hall, assuming $3.5\ \text{m}^3$ of air is required for each person.
4. 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 $\pi \approx \frac{22}{7}$.
5. Height of a cuboid from its edges ●○○○○ 10 ptsA cuboid has a base measuring 8 cm by 10 cm. The total length of all its edges is 92 cm. Find the height of the cuboid in centimetres.
6. Cylinder cut from a cuboid ●●○○○ 20 ptsA cylinder of maximum volume is cut from a wooden cuboid of length 30 cm whose cross-section is a square of side 14 cm. Use $\pi = \frac{22}{7}$. Find the volume of the cylinder (in cm³) and the volume of wood wasted (in cm³).
7. Bricks painted by a container ●●○○○ 20 ptsA container has enough paint to cover an area of $9.375$ m$^2$. Each brick measures $22.5$ cm by $10$ cm by $7.5$ cm, and its whole surface is painted. How many such bricks can be painted with the paint in the container?
8. Bricks that a container of paint covers ●●○○○ 20 ptsA container of paint is enough to paint an area of $9.375\ \text{m}^2$. Each brick measures $22.5\ \text{cm} \times 10\ \text{cm} \times 7.5\ \text{cm}$. Assuming the whole surface of each brick is painted, how many bricks can be painted with this paint?
9. Cuboid of minimal surface area ●●●○○ 50 ptsA juice box is a rectangular box (cuboid) with volume $200\ \text{cm}^3$ ($200$ ml). Find the length $l$, width $w$ and height $h$ (in cm) of the box with the least possible surface area. Round each answer to five decimal places.
10. Longest edge of a rectangular block ●●●○○ 50 ptsThe lengths of three unequal edges of a rectangular solid block are in geometric progression. The volume of the block is $216\ \text{cm}^3$ and its total surface area is $252\ \text{cm}^2$. Find the length of the longest edge, in cm.