Question

the volume of a pyramid that fits exactly inside a cube is 18 cubic feet. what is the volume of the cube? 6 cubic feet 18 cubic feet 54 cubic feet 72 cubic feet question 4 (multiple choice worth 1 point) (08.03 mc) pyramid a is a square pyramid with a base side length of 8 inches and a height of 9 inches. pyramid b has a volume of 2,880 in³. how many times bigger is the volume of pyramid b than pyramid a? 15 32 54 75 question 5 (multiple choice worth 1 point) (08.03, 08.04 mc) bridget has a kitchen canister in the shape of a cylinder, which holds flour. if the canister is 24 cm in diameter and 26 cm tall, what is the surface area of the cylinder in terms of π? 624π cm² 1,248π cm² 912π cm² 1,296π cm²

Explanation:

Step1: Relate pyramid and cube volume

For a pyramid fitting exactly in a cube, its volume is $\frac{1}{3}$ of the cube's volume. Let $V_{cube}$ = volume of cube, $V_{pyramid}=18$.
$V_{pyramid} = \frac{1}{3}V_{cube}$

Step2: Solve for cube volume

Rearrange to solve for $V_{cube}$:
$V_{cube}=3\times V_{pyramid}=3\times18=54$

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Step1: Calculate volume of Pyramid A

Pyramid A is square-based: $V_A=\frac{1}{3}\times \text{base area}\times \text{height}$. Base area $=8^2=64$, height=9.
$V_A=\frac{1}{3}\times64\times9=192$

Step2: Find ratio of volumes

Divide $V_B$ by $V_A$: $\frac{V_B}{V_A}=\frac{2880}{192}=15$

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Step1: Find radius of cylinder

Diameter=24 cm, so radius $r=\frac{24}{2}=12$ cm, height $h=26$ cm.

Step2: Total surface area formula

Total surface area of cylinder: $SA=2\pi r^2 + 2\pi r h$

Step3: Substitute values

$SA=2\pi(12)^2 + 2\pi(12)(26)=2\pi(144)+2\pi(312)=288\pi+624\pi=912\pi$

Answer:

1. 54 cubic feet
2. 15
3. $912\pi \text{ cm}^2$