Two similar vases have heights which are in the ratio 3 : 2.
(a) The volume of the larger vase is 1080 cm cube. Calculate the volume of the smaller vase.
(b) The surface area of the smaller vase is 252cm square. Calculate the surface area of the larger vase.

Answer:

a). Volume of the smaller vase = 320 cm³

b). Surface area of the larger vase = 567 cm²

Step-by-step explanation:

When we calculate the volume of any figure we multiply it's three dimensions either length, width, height or we do the cube of the radius (r×r×r=r³).

In other words volume is a three dimensional figure and surface area is two dimensional.

Therefore, ratio of volumes of two similar structures will be the ratio of cube of one side given.

a). [tex]\frac{V_{1}}{V_{2} }=(\frac{Side 1}{Side2})^{3}[/tex]

[tex]\frac{V_{1}}{V_{2} }=(\frac{3}{2})^{3}[/tex]

[tex]\frac{1080}{V_{2} }=(\frac{3}{2})^{3}[/tex]

[tex]\frac{1080}{V_{2} }=(\frac{27}{8})[/tex]

[tex]27V_{2}=8\times 1080[/tex]

[tex]V_{2}=\frac{8640}{27}[/tex]

[tex]V_{2}=320[/tex] cm³

b). Similarly ratio of the surface area of two vase will be

[tex]\frac{A_{1}}{A_{2} }=(\frac{Side 1}{Side2})^{2}[/tex]

[tex]\frac{A_{1}}{252}=(\frac{3}{2})^{2}[/tex]

[tex]\frac{A_{1}}{252}=(\frac{9}{4})[/tex]

[tex]A_{1}=\frac{9\times 252}{4}[/tex]

[tex]A_{1}=567[/tex] cm²

The standard height of kitchen cabinets is 34.5 inches. What is the metric equivalent in centimeters?

2/3n + 5 greater than 12

15-(m+p);use m=3,and p=10

What number must multiply each side of the equation 2/3x = 16 to produce the equivalent equation x = 24?

- 2/3

2/3

- 3/2

3/2

450 is 75.2% of what number?

A projectile is thrown upward so that its distance above the ground after t seconds is given by the function h(t) = - 16t^2 + 576t. After how many seconds does the projectile take to reach its maximum height? Show your work for full credit.

Millie designed a rectangular label to put on the front of her scrapbook. The label was 5/12 foot wide and 5/6 foot long. What was the area in square feet of the label ?

Lines AB and CD are parallel. If 1 measures 131°, what is the measure of 4?
A.
141°
B.
59°
C.
49°
D.
131°

Sarah,Juan, are on the track team. Last week, Sarah ran 8.25 miles, Juan ran 11.8 miles, and Larry ran 9.3 miles. How many miles did they run altogether?

olive bought 36 potatoes plants. She planted them in her garden in 4 even rows. Wild animals ate a row. 5 plants were eaten by sheep and 2 by a goat in the same row. How many plants were remaining in the row that sheep and goat got to? answer<br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br />

Jonathan purchased 30 bags of mulch to spread in his garden. The graph shows points representing the number of bags of mulch left to spread at several different times while Jonathan is working.

A function graph of a line segment having three points (0,30), (1,21) and (2, 12) with an x axis of zero to four Hours and a y axis of zero to thirty five Bags of mulch left



Select from the drop-down menus to complete the equation, in standard form, that represents the relationship between the number of bags of mulch left to spread, y, and the time, x, Jonathan has spent mulching.

Josie spent 4/7 of the money in her purse on some books, and the rest of the money on 18 markers. Each marker cost $1.20. How much money was in Josie's purse to begin with?

maddie's bank account the time(hours) and Amount in account($) the order paris are (0,40),(1,49),(2,58),(3,67) what is the rate

. If x = 5 units, y = 17 units, and z = 4 units, then what is the surface area of the rectangular prism shown above? A. 340 units2 B. 346 units2 C. 414 units2 D. 173 units2

plz help for question 23

Suppose instead that you have 1 1/2 apples. If this is enough to make 3/5 of an adult serving, how many apples (and parts of an apple) make up one adult serving?

Lynnette can wash 95 cars in 5 days. How many cars can Lynnette wash in 11 days?

How do you do this. I really need help.

One-half of a roll of wallpaper covers 1/10 of a wall. How many rolls of wallpaper are needed to cover half the wall?

Hubert is stacking canned vegetables on shelves in a warehouse. Eight cans of corn are packed in each box.If Hubert puts 56 boxes of corn and 92 boxes of beets on the shelves , how many cans of vegetables are on the shelves?

A geologist visits 60 volcanoes in Alaska and California. 15% of the volcanoes are in California. How many volcanoes did the geologist visit in California and how many are in Alaska?

Janette went to Tire Mart and paid $122.57 per tire for 4 tires and a flat rate fee for installation for a total of $555.28 before taxes. Monique went to Fast Wheels and paid $136.71 per tire for 4 tires and a flat rate fee for installation for a total of $585.34 before taxes. The difference in the amount that they paid in installation charges is $.

for questions 1-5 estimate the sum or difference.

1. 9/10 + 7/8
A) 1
B)2
C)0

2. 9/50 + 7/15
A)0
B) 1/2
C) 1

3. 2/8/9 - 2/1/7

A) 2
B) 1
C) 0

4. 8/12/31 + 4/5/6

A) 13
B) 12/1/2
C) 14

5. 15/2/15 - 15/1/20

A)2
B) 1
C) 0

1/7 of the power of three

What is the value of x in this proportion, 6/9 = x/12

Four teachers bought 10 origami books and 100 packs of oragami paper for their classrooms. They will share the cost of the items equally. How much should each teacher pay?

What is the range of the function on the graph?

A.all real numbers
B.all real numbers greater than or equal to 0
C.all real numbers greater than or equal to 1
D.all real numbers greater than or equal to 2

The cafeteria at midtown middle school surveyed 575students about the favorite food.Find the number of students that responded for each of the following...

Eric says he knows 9/10 is 1/10 less than 10/10 or 1 mile so he is going to subtract 1 mile then I had 1/10 back can he use this method to solve the example problem explain

Write 39,083 in word form