Notice the exponents in these two statements.
Those little tiny numbers tell the whole big story:
(the ratio of the surface areas of similar figures) = (the ratio of their linear dimensions)2
(the ratio of the volumes of similar solids) = (the ratio of their linear dimensions)3
A cone, a cylinder and a sphere would fit the given description
A triangular prism and a pentagonal based pyramid would fit the given description.
surface area of a cylinder? No. In 2-dimensional space, a circle and in 3-d, a sphere.
It is a cylinder that fits the given description.
Perimeter will scale by the same factor. Area of the new figure, however is the original figures area multiplied by the scale factor squared. .
A cone, a cylinder and a sphere would fit the given description
A triangular prism and a pentagonal based pyramid would fit the given description.
surface area of a cylinder? No. In 2-dimensional space, a circle and in 3-d, a sphere.
A square normally consists of two dimensions, length and width. In order to determine how big a dimensional square is, we need to have exact figures given to us, so we can produce result in terms of numbers.
It is a cylinder that fits the given description.
The set of all points a given distance from a center point is a circle. The given distance is the radius, and the given point is the center. In 3 dimensional space, the set would be the surface of a sphere.
A square normally consists of two dimensions, length and width. In order to determine how big a dimensional square is, we need to have exact figures given to us, so we can produce result in terms of numbers.
Perimeter will scale by the same factor. Area of the new figure, however is the original figures area multiplied by the scale factor squared. .
A square normally consists of two dimensions, length and width. In order to determine how big a dimensional square is, we need to have exact figures given to us, so we can produce result in terms of numbers.
The ratio of the surface areas of two similar figures is equal to the square of the ratio of their corresponding linear dimensions. Given the surface areas are 27 and 1331, the ratio of their corresponding linear dimensions is the square root of ( \frac{1331}{27} ). Since the volume ratio is the cube of the linear dimension ratio, we can find the larger volume by calculating ( \frac{1331}{27} ) and then multiplying the smaller volume (18) by the cube of that ratio. The larger volume is therefore ( 18 \times \left(\frac{1331}{27}\right)^{\frac{3}{2}} = 486 ).
They do not know the population of Pompeii. Any figures given out are just estimates as there were no population records for the town.They do not know the population of Pompeii. Any figures given out are just estimates as there were no population records for the town.They do not know the population of Pompeii. Any figures given out are just estimates as there were no population records for the town.They do not know the population of Pompeii. Any figures given out are just estimates as there were no population records for the town.They do not know the population of Pompeii. Any figures given out are just estimates as there were no population records for the town.They do not know the population of Pompeii. Any figures given out are just estimates as there were no population records for the town.They do not know the population of Pompeii. Any figures given out are just estimates as there were no population records for the town.They do not know the population of Pompeii. Any figures given out are just estimates as there were no population records for the town.They do not know the population of Pompeii. Any figures given out are just estimates as there were no population records for the town.
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.