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My sister’s birthday is in a few weeks and I would like to buy her a new vase to keep fresh flowers in her house. She often forgets to water her flowers and needs a vase that holds a lot of water. In a catalog, there are three vases available and I want to purchase the one that holds the most water. The first vase is a cylinder with diameter 10 cm and height 40 cm. The second vase is a cone with base diameter 16 cm and height 45 cm. The third vase is a sphere with a diameter of 18 cm.

1. Find the volume for each vase.

2. Which vase should I purchase?

3. How much more water does the largest vase hold than the smallest vase?

4. Suppose the diameter of each vase decreases by 2 cm. Which vase would hold the most water?

Respuesta :

djstein02p8piub

Answer:

1. 392, 20.83, 4/3

2. 16 cm and 45 cm cone

3. 0.9 Fl oz

4. the cone still

Step-by-step explanation:

The volume of each vase can be determine by using volume formula of sphere, cone and cylinder.

(1) The volume of sphere is [tex]972\pi[/tex], volume of cone is [tex]960\pi[/tex] and volume of cylinder is [tex]1000\pi[/tex].

(2) You should purchase the cylinder vase.

(3) The largest vase hold [tex]40 \pi \:{\rm cm}^3[/tex] more than smallest vase.

(4) If the diameter decreases by 2 cm, then cone holds more water.

Given:

Diameter of cylinder is [tex]d=10 \:\rm cm[/tex].

Height of cylinder is [tex]h=40\:\rm cm[/tex].

Diameter of cone is [tex]d=16 \:\rm cm[/tex].

Height of cylinder is [tex]h=45\:\rm cm[/tex].

Diameter of sphere is [tex]d=45 \:\rm cm[/tex].

(1)

Calculate the volume of cylinder.

[tex]\begin{aligned}\mbox{Cylinder Volume} &= \pi r^2 h\\& = \pi(5)^2(40) \text{ cm}^3\\&= 1000 \pi \text{ cm}^3.\end{align}[/tex]

Calculate the volume of Cone.

[tex]\begin{aligned}\mbox{Cone Volume} &= \frac13 \pi r^2 h\\&= \frac13 \pi(8)^2(45) \text{ cm}^3\\&= 960 \pi \text{ cm}^3.\end{align}[/tex]

Calculate the volume of sphere.

[tex]\begin{aligned}\mbox{Sphere Volume} &= \frac43 \pi r^3\\&= \frac43 \pi (9)^3 \text{ cm}^3\\&= 972 \pi \text{ cm}^3.\end{align}[/tex]

(2)

Since the volume of cylinder is higher than the volume of sphere and cone. So, you should purchase cylinder vase.

(3)

The largest vase hold water more than the smallest vase is,

[tex]\text{Cylinder Volume} - \text{Cone Volume} = 1000 \pi \text{ cm}^3 - 960 \pi \text{ cm}^3 = 40 \pi \text{ cm}^3[/tex]

(4)

As per the question if diameter of each vase decreases by 2 cm then radius decreases by 1 cm.

Calculate the volume of cylinder.

[tex]\begin{aligned}\mbox{Cylinder Volume} &= \pi r^2 h\\&= \pi(4)^2(40) \text{ cm}^3\\&= 640 \pi \text{ cm}^3.\end{align}[/tex]

Calculate the volume of Cone.

[tex]\begin{aligned}\mbox{Cone Volume}&= \frac13 \pi r^2 h\\&= \frac13 \pi(7)^2(45) \text{ cm}^3\\&= 735 \pi \text{ cm}^3.\end{align}[/tex]

Calculate the volume of sphere.

[tex]\begin{aligned}\mbox{Sphere volume} &= \frac43 \pi r^3\\&= \frac43 \pi (8)^3 \text{ cm}^3\\&= 682 \frac23 \pi \text{ cm}^3.\end{align}[/tex]

Since the volume of cone is more the sphere and cylinder. So cone hold most water.

Learn more about volume here:

https://brainly.com/question/8667621

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