MATH SOLVE

5 months ago

Q:
# 1. Lisa wanted to paint her ugly brown flower box red. Using the given dimensions, how many square inches will she have to paint? Dimensions: 22x10x36 2. Tom is trying to wrap a present for his mother’s birthday. The box is 8.5 inches wide, 12 inches long, and 4 inches high. How much wrapping paper will he need? 3. David and Karen are building a tree house for their daughter. If the tree house is going to 5 feet tall, 8 feet wide, and 7.5 feet long how much space will there be inside? How much space will they have to paint on the outside? 4. This pencil cup is made out of plastic. It is 5 inches tall and has a radius of 1.75 inches. How many square inches of plastic were used to make the cup? 5. A Campbell’s Soup can is 6 inches tall and has a radius of 2.5 inches. How much paper is needed to make the label? How much room

Accepted Solution

A:

1. Given that the box is the form of a rectangular prism and that the dimensions are 22 x 10 x 36 (l x w x h):

Surface area = 2wh + 2lh + 2wl

= 2(wh + lh + wl)

= 2(10*36 + 22*36 + 10*22)

= 2(360 + 792 + 220)

= 2*1372

= 2744 in^2

2. This question is similar to the one above:

Surface area = 2(wh + lh + wl)

= 2(8.5*4 + 12*4 + 8.5*12)

= 2(34 + 48 + 102)

= 2*184

= 368 in^2

3. The space that there will be inside the tree house is equivalent to its volume:

Volume of a rectangular prism = lwh

= 7.5*8*5

= 300 ft^3

The space that there will be to paint on the outside is equivalent to the tree house's surface area:

Surface area of a rectangular prism = 2(wh + lh + wl)

= 2(8*5 + 7.5*5 + 8*7.5)

= 2(40 + 37.5 + 60)

= 2*137.5

= 275 ft^2

4. Assuming the cup is in the form of a cylinder and has an open top:

Surface area = πr^2 + 2πrh

= π*1.75^2 + 2π*1.75*5

= 3.0625π + 17.5π

= 20.5625π in^2

= 64.599 in^2 (to three decimal places)

5. The general formula for the surface area of a cylinder is 2πr^2 + 2πrh, where 2πr^2 is the area of the two circles and 2πrh is the area of the rectangular bit that is inbetween (or in this case the label of the soup can), thus:

Area of label = 2πrh

= 2π*2.5*6

= 30π in^2

= 94.248 in^2 (to three decimal places)

I am assuming the last questions asks 'How much room is there inside the can?' - if so, then the room would be equivalent to the volume of the can, thus:

Volume of cylinder = πr^2*h

= π*2.5^2*6

= 37.5π in^3

= 117.810 in^3 (to three decimal places)

Surface area = 2wh + 2lh + 2wl

= 2(wh + lh + wl)

= 2(10*36 + 22*36 + 10*22)

= 2(360 + 792 + 220)

= 2*1372

= 2744 in^2

2. This question is similar to the one above:

Surface area = 2(wh + lh + wl)

= 2(8.5*4 + 12*4 + 8.5*12)

= 2(34 + 48 + 102)

= 2*184

= 368 in^2

3. The space that there will be inside the tree house is equivalent to its volume:

Volume of a rectangular prism = lwh

= 7.5*8*5

= 300 ft^3

The space that there will be to paint on the outside is equivalent to the tree house's surface area:

Surface area of a rectangular prism = 2(wh + lh + wl)

= 2(8*5 + 7.5*5 + 8*7.5)

= 2(40 + 37.5 + 60)

= 2*137.5

= 275 ft^2

4. Assuming the cup is in the form of a cylinder and has an open top:

Surface area = πr^2 + 2πrh

= π*1.75^2 + 2π*1.75*5

= 3.0625π + 17.5π

= 20.5625π in^2

= 64.599 in^2 (to three decimal places)

5. The general formula for the surface area of a cylinder is 2πr^2 + 2πrh, where 2πr^2 is the area of the two circles and 2πrh is the area of the rectangular bit that is inbetween (or in this case the label of the soup can), thus:

Area of label = 2πrh

= 2π*2.5*6

= 30π in^2

= 94.248 in^2 (to three decimal places)

I am assuming the last questions asks 'How much room is there inside the can?' - if so, then the room would be equivalent to the volume of the can, thus:

Volume of cylinder = πr^2*h

= π*2.5^2*6

= 37.5π in^3

= 117.810 in^3 (to three decimal places)