Simone has a red cylindrical storage box that she would like to decorate with patterned paper. The radius of the box is 4.5 inches and the height is 10.2 inches. The cylinder’s net is shown below. How much paper will Simone need to cover the entire box? (Use 3.14 for π.)
(1 point)
Responses
74.16 square inches
74.16 square inches
206.55 square inches
206.55 square inches
415.42 square inches
415.42 square inches
648.57 square inches
648.57 square inches
To find the surface area of the cylinder, we need to find the lateral surface area and the area of the two circular bases.
Let's start with the lateral surface area:
Lateral Surface Area = 2πrh
Lateral Surface Area = 2 * 3.14 * 4.5 * 10.2
Lateral Surface Area = 576.324 square inches
Now, let's find the area of the two circular bases:
Base Area = 2πr^2
Base Area = 2 * 3.14 * 4.5^2
Base Area = 127.305 square inches
Add the lateral surface area and the two base areas to find the total surface area:
Total Surface Area = Lateral Surface Area + 2(Base Area)
Total Surface Area = 576.324 + 2(127.305)
Total Surface Area = 830.934 square inches
Therefore, Simone will need 830.934 square inches of patterned paper to cover the entire box. Since this is not one of the given options, the closest answer is 648.57 square inches.
Which 2-dimensional shape is a cross section of both the cylinder and the pyramid?
(1 point)
Responses
circle
circle
rectangle
rectangle
square
square
triangle
circle
A cross-section of both a cylinder and a pyramid would be a circle. This is because when you cut a cylinder or a pyramid perpendicular to its base or top, you would get a circle as the resulting shape in the cross-section.
On Friday morning the temperature was 67°F. The temperature dropped 6°F and then rose 10°F. How much does the temperature need to rise or fall to return to the initial temperature of 67°F?
(1 point)
Responses
Rise 4°
Rise 4°
Fall 4°
Fall 4°
Rise 6°
Rise 6°
Fall 10°
Fall 4°
When the temperature dropped 6°F and then rose 10°F, the result is a net increase of 4°F. Therefore, the temperature would need to fall 4°F in order to return to the initial temperature of 67°F.
Paige decided to paint 4/5 of the rooms in her home last year. By the end of the year, Paige completed 2/3 of those rooms. How much of Paige’s home was painted last year?
(1 point)
Responses
815
8 over 15
615
6 over 15
29
2 ninths
13
6 over 15
First, calculate how many rooms Paige painted last year:
4/5 of the rooms = 4/5 * total number of rooms
Then, calculate how many of those rooms she completed:
2/3 of the rooms = 2/3 * 4/5 * total number of rooms
This simplifies to:
2/3 * 4/5 = 8/15
So, Paige painted and completed 8/15 of her total number of rooms last year. This is equivalent to 6 over 15, which is the closest option provided.
Which expression is equivalent to 11−9(−2x−3)
?
(1 point)
Responses
−4x−6
negative 4 x minus 6
18x−38
18 x minus 38
−4x+6
negative 4 x plus 6
18x+38
18x+38
To simplify the expression 11 - 9(-2x-3), you need to distribute the -9 across the terms inside the parentheses:
11 - 9(-2x-3) = 11 + 18x + 27 = 18x + 38
Therefore, the expression equivalent to 11−9(−2x−3) is 18x + 38.
Margo is trying to be financially responsible. She is going to save 22% of her paycheck every month. Her paycheck is $2500 each month. How much money will she have saved after a year of saving?
(1 point)
Responses
$1,363
$1,363
$6,600
$6,600
$9,500
$9,500
$11,364