Before a supply ship left for Mars, Nova and Luna had to arrange cargo inside a compartment 4 meters wide, 3 meters high, and 6 meters long. Four cylindrical tanks, each 1 meter in diameter and 3 meters long, initially laying across the floor. Luna suggested turning the cylinders so their 3-meter lengths matched the compartment's height. Each cylinder then occupied a 1-meter by 1-meter section of floor space. Nova calculated that each tank's volume was 0.75π cubic meters and checked its curved and circular surfaces to plan secure straps. The remaining floor could now hold rectangular crates measuring 2 meters by 1 meter by 1 meter much more efficiently. After comparing the dimensions, cross-sections, and usable space in both arrangements, Nova and Luna chose the second layout. The cargo fit securely, and the supply ship departed for Mars on schedule.

Challenges

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Challenge 1 of 5

Challenges

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Challenge 1 of 4
Hint
For a cylinder, use its radius, not its diameter, in the formula πr^2h.
Each cylindrical tank has a diameter of 1 meter and a length of 3 meters. Which calculation correctly gives the volume of one tank?
π(1)^2(3) = 3π cubic metersπ(0.5)^2(3) = 0.75π cubic meters2π(0.5)(3) = 3π cubic metersπ(0.5)(3) = 1.5π cubic meters
Correct. The radius is 0.5 meter, so the volume is 0.75π cubic meters.
First convert the 1-meter diameter to a radius, then use the cylinder volume formula.
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Hint
Find the total floor area, then subtract the floor sections occupied by all four tanks.
In the second layout, each of the four upright tanks occupies a 1-meter by 1-meter section of the compartment floor. The compartment floor is 4 meters by 6 meters. How many square meters of floor space remain outside the four tank sections?
Correct. The compartment has 24 square meters of floor area, and the four tank sections occupy 4 square meters.
Calculate the 4-meter by 6-meter floor area first, then subtract four 1-meter by 1-meter sections.
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Hint
The tank's radius is half its 1-meter diameter. Compare πr^2 with the area of the 1-meter by 1-meter square.
Nova compares the actual circular base of one upright tank with the 1-meter by 1-meter floor section reserved for it. Which statement correctly explains why some space inside that square section is not part of the tank's circular base?
The circle has area π square meters, which is greater than the 1-square-meter section.The circle and square both have area 1 square meter, so no space remains.The circle has area 0.25π square meters, which is less than the square's area of 1 square meter.The circle has area 0.5π square meters, which is exactly half the square's area.
Correct. The circular base has area 0.25π square meters, which is less than 1 square meter.
Use a radius of 0.5 meter to find the circular base area, then compare it with the 1-square-meter section.
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Mars Görevi İçin Kargo
TR
ARC_G10_GM_02_STORY_02
Mars Görevi İçin Kargo
Cargo for the Mars Mission
EN
ARC_G10_GM_02_STORY_02
Cargo for the Mars Mission