Anonymous
Anonymous asked in Science & MathematicsMathematics · 6 years ago

Would you please explain what I am doing wrong on these questions; and how to solve them correctly.?

1. Gino designed a garden for his rectangular backyard. The design he drew on paper is ten inches long. The length of his backyard is fifty feet. If his drawing is to scale and is 9 inches wide, how many feet wide is his backyard? Write a proportion using words. Then, use the proportion to calculate the yard width. Show your work.

My Answer: 10 inches is to 50 feet as 9 inches is to x feet.

10/50 = 9/x or (10 over 50 & 9 over x)

Then you will cross multiply.

10x = 50 x 9

10x = 500

10x/10 = 500/10

x = 50 feet

So Gino`s backyard is 50 feet wide.

2. Evan is painting a stool that has a cylindrical seat and four rectangular prism legs. The seat has a diameter of fourteen inches and a height of 4 inches. Each leg is 4 inches by 4 inches by eighteen inches. How much area will Evan have to paint? Use three point one four for pi. Show your work.

My Answer: The surface area for the top and bottom of the seat is: 2 x 3.14 x 14 x 14 = 1,230.88 inches

1,230.88/4 = 307.72

The diameter for the seat is: 3.14 x 14 x 4 = 175.84 inches

The total area of the seat is: 307.72 + 175.84 = 483.56 inches

The area of the 4 legs is: 4 x (2 x 4 x 4) = 32 inches

& 4 x 4 x 18 = 288

288 + 32 = 320 & 320 x 4 = 1,280 for the area that Evan will have to paint.

3. The volume of a cone is three hundred cubic kilometers. If the radius of the base is 6 kilometers, what is the height of the cone?

3 Answers

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  • Ash
    Lv 7
    6 years ago
    Best Answer

    1) You started correctly. But look at the error below..... 50 x 9 = 450 and not 500. Once you correct that the width will be 45 feet

    ------------------

    "10x = 50 x 9

    10x = 500"

    -----------------

    2) Evan will have paint the the top of the seat, bottom of the seat and the periphery of the seat. Additional the 4 legs.

    However, have you considered that one of the leg face attached to the seat will not have to be painted. And that same area has to be deducted from the bottom of the seat.

    Area of top face of the 4 legs = 4x (4 x 4) = 32 in²

    Total area of the seat = 483.56 in²

    Total area of the seat to be painted = 483.56 - 32 = 451.56 in²

    Similary

    Area of all faces of 4 legs = 1,280 in ²

    Area of all faces of the legs to be painted = 1280 - 32 = 1248 in ²

    Grand total area to be painted = 451.56 + 1248 = 1699.56 in²

    3) Volume of cone (V)= (1/3) π r² h

    h = 3V/π r² = (3 * 300) / (3.14 * 6²) = 7.96 km

  • 6 years ago

    9 x 50 is not 500 its 450

    so 45 feet

    Second one :Your Answer: The surface area for the top and bottom of the seat is: 2 x 3.14 x 14 x 14.

    14 x 14 is diameter squared, it should be radius squared so 7 x 7

    third is 7.96

  • 6 years ago

    1. Gino designed a garden for his rectangular backyard. The design he drew on paper is ten inches

    long. The length of his backyard is fifty feet. If his drawing is to scale and is 9 inches wide, how

    many feet wide is his backyard? Write a proportion using words. Then, use the proportion to

    calculate the yard width. Show your work. 

    The proportion of the length on paper divided by the actual length (with a unit conversion)

    is identical to the proportion of the width on paper divided by the actual width (again with a unit

    conversion).

    50 ft = 50 ft x 12 in/ft = 600 in

    10/600 = 9/p

    10p = 9 x 600

    10p = 5,400

    p = 5,400/10

    p = 540 in = 540 in / 12 in/ft = 45 ft Width of Gino's back yard

    2. Evan is painting a stool that has a cylindrical seat and four rectangular prism legs. The seat has

    a diameter of fourteen inches and a height of 4 inches. Each leg is 4 inches by 4 inches by eighteen

    inches. How much area will Evan have to paint? Use three point one four for pi. Show your work. 

    Surface Area of Cylindrical Seat

    Top Area

    A = πD²/4 = (3.14)(14 in)²/4 = 153.86 in²

    Bottom Area

    A = πD²/4 = (3.14)(14 in)²/4 = 153.86 in²

    Circumference Area

    C = πD = (3.14)(14 in) = 43.96 in

    h = 4 in

    A = Ch = (43.96 in)(4 in) = 175.84 in²

    A(tot) = 153.86 in² + 153.86 in² + 175.84 in² = 483.56 in²

    Surface Area of Legs

    Top Area

    A = s² = (4 in)² = 16 in²

    Bottom Area

    A = s² = (4 in)² = 16 in²

    Side of Leg

    A = 4 in x 18 in = 72 in²

    4 Sides

    A = 4(72 in) = 288 in²

    Leg (1)

    A = 16 in² + 16 in² + 288 in² = 320 in²

    4 Legs

    A = 4(392 in²) = 1,280 in²

    Total Surface Area of Stool

    A = 483.56 in² + 1,280 in² = 1,763.56 in² AREA TO BE PAINTED

    3. The volume of a cone is three hundred cubic kilometers. If the radius of the base is 6 kilometers,

    what is the height of the cone?

    V = volume = 300 km³

    r = radius of the base = 6 km

    V = πr²h/3

    3V = πr²h

    3V/πr² = h

    h = 3V/πr²

    h = 3(300 km³)/π(6 km)²

    h = 7.96 km HEIGHT OF THE CONE

    • 6 years agoReport

      Thank you very much!

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