<span>I chose a box of cereal-------> rectangular prism
</span>see the attached figure
Part 1)<span>List the dimensions of your box. Be sure to include the units (in, cm, ft, etc.).
Length: 20 cm
Width: 8 cm
Height: 32 cm
Part </span><span>
2). Describe the shape of the cross-section when the box is cut parallel to the base
the shape of the </span>cross-section <span>would be a rectangle of dimensions
20 cm x 8 cm
Part 3)</span><span>What is the surface area of the box?
</span>
surface area=2*area of the base+perimeter of the base*height
area of the base=20*8=160 cm²
perimeter of the base=2*[20+8]-----> 56 cm
height=32 cm
surface area=2*160+56*32------> 2,112 cm²
the answer part 3) is2,112 cm²Part 4)<span>What is the surface area of the box if it is scaled up by a factor of 10?
</span>
we know that
surface area of the larger box=[scale factor]²*surface area original box
scale factor=10
surface area original box=2,112 cm²
so
surface area of the larger box=10²*2,112-----> 211,200 cm²
the answer part 4) is211,200 cm²Part 5) <span>What is the volume of the box?
</span>
volume of the box=L*W*H-----> 20*8*32------> 5,120 cm³
the answer Part 5) is5,120 cm³Part 6) <span>What is the volume of the box if it is scaled down by a factor of 1/10
we know that
volume of the smaller box=[scale factor]</span>³*volume original box
scale factor=1/10
volume original box=5,120 cm³
so
volume of the smaller box=[1/10]³*5,120-----> 5.12 cm³
the answer part 6) is5.12 cm³
