The squared area of the box, from the question itself, is 61 square inches. Scaling up the linear dimensions by a factor of 10 will make the area 6100 square inches.
No.
No.
To find the surface area of the smaller figure, we can use the relationship between the volumes and surface areas of similar figures. The volume ratio of the larger figure to the smaller figure is ( \frac{2744}{729} = \left(\frac{a}{b}\right)^3 ), where ( a ) is the linear dimension of the larger figure and ( b ) is that of the smaller figure. Taking the cube root gives the linear scale factor ( \frac{a}{b} = \frac{14}{9} ). The surface area ratio, which is the square of the scale factor, is ( \left(\frac{14}{9}\right)^2 = \frac{196}{81} ). Given the surface area of the larger figure is 392 mm², the surface area of the smaller figure is ( 392 \times \frac{81}{196} = 162 ) mm².
9xy(3xy - 4)
Nothing. The cylinder's surface area does not have a GCF.
No. That isn't possible: A prime number, by definition, has no smaller factors. A square number does have a smaller factor - the number that is squared.
The squared area of the box, from the question itself, is 61 square inches. Scaling up the linear dimensions by a factor of 10 will make the area 6100 square inches.
Assuming the smaller sphere is the image of the larger sphere after transformation (based on the order of the radii): the scale factor is 4/12 = 1/3
cheese
No.
No.
To find the surface area of the smaller figure, we can use the relationship between the volumes and surface areas of similar figures. The volume ratio of the larger figure to the smaller figure is ( \frac{2744}{729} = \left(\frac{a}{b}\right)^3 ), where ( a ) is the linear dimension of the larger figure and ( b ) is that of the smaller figure. Taking the cube root gives the linear scale factor ( \frac{a}{b} = \frac{14}{9} ). The surface area ratio, which is the square of the scale factor, is ( \left(\frac{14}{9}\right)^2 = \frac{196}{81} ). Given the surface area of the larger figure is 392 mm², the surface area of the smaller figure is ( 392 \times \frac{81}{196} = 162 ) mm².
The GCF is 7mn.
The GCF is 4.
9xy(3xy - 4)
(5x - 2y)(5x + 2y)