Respuesta :
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)
