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How does the perimeter change when the dimensions are changed by a scale factor of 3?
The perimeter, being a linear measure, also changes by a factor of 3.
What happens to the Surface Area and Volume of a pyramid if the radius and height are divided by 2?
The surface area is reduced by a factor 4, the volume by a factor 8.
What would happen if the dimensions of a cone doubled?
If the dimensions of a cone are doubled, both its height and radius increase by a factor of two. As a result, the volume of the cone, which is calculated using the formula ( V = \frac{1}{3} \pi r^2 h ), would increase by a factor of eight, since volume is proportional to the cube of the dimensions. The surface area would also increase, but by a smaller factor of four, as surface area scales with the square of the dimensions. Thus, the cone would become significantly larger in both volume and surface area.
When both dimensions of a figure are changed using the same scale factor is the change proportional or non proportional?
If it is a 2-dimensional figure then it is proportional.
If the dimension of the rectangular prism are quadrupled the surface area will increase 8 times true or false?
False. If the dimensions of a rectangular prism are quadrupled, the surface area will increase by a factor of 16, not 8. This is because surface area is proportional to the square of the dimensions, so if each dimension is multiplied by 4, the surface area increases by (4^2 = 16).
When the volume and the surface area of a cylinder with radius R units and height H units. Now assume that the dimensions of the cylinder are tripled- In that case what would be the dimensions of the?
Volume = area circular end × height = πR²H units³ Surface area = 2 × area of circular end + area of curved side = 2πR² + 2πRH units² = 2πR(R + H) units² If lengths are changed by a scale factor of n, areas are changed by a scale factor of n² and volumes are changed by a scale factor of n³. If the dimensions are tripled, the new volume is 3³πR²H units³ = 27πR²H units³ The new surface area is 3²×2πR(R + H) units² = 18πR(R + H) units²
How does the perimeter change when the dimensions are changed by a scale factor of 3?
The perimeter, being a linear measure, also changes by a factor of 3.
What happens to the Surface Area and Volume of a pyramid if the radius and height are divided by 2?
The surface area is reduced by a factor 4, the volume by a factor 8.
When all dimensions are tripled what happens to the volume?
If linear dimensions are increased by a certain factor, the volume will increase by that same factor, raised to the third power - so, in this case, 3 to the power 3.
What would happen if the dimensions of a cone doubled?
If the dimensions of a cone are doubled, both its height and radius increase by a factor of two. As a result, the volume of the cone, which is calculated using the formula ( V = \frac{1}{3} \pi r^2 h ), would increase by a factor of eight, since volume is proportional to the cube of the dimensions. The surface area would also increase, but by a smaller factor of four, as surface area scales with the square of the dimensions. Thus, the cone would become significantly larger in both volume and surface area.
What happens to the Surface Area of a cube if each edge is multiplied by 7?
The surface area increase by a factor of 49.
When both dimensions of a figure are changed using the same scale factor is the change proportional or non proportional?
If it is a 2-dimensional figure then it is proportional.
What happens to the greatest common factor of the cylinders' surface area if its radius is squared?
Nothing. The cylinder's surface area does not have a GCF.
If the dimension of the rectangular prism are quadrupled the surface area will increase 8 times true or false?
False. If the dimensions of a rectangular prism are quadrupled, the surface area will increase by a factor of 16, not 8. This is because surface area is proportional to the square of the dimensions, so if each dimension is multiplied by 4, the surface area increases by (4^2 = 16).
If the dimensions of a figure are increased by a factor of 7 By what factor does the volume change?
if all 3 dimensions increase b factor of 7 then volume changes by 7 cubed or a factor of 343
How does the perimeter of a figure change if the dimensions are changed from yards o feet?
The absolute value of the perimeter doesn't change, only the unit value which increases by a factor of 3.
If all the dimensions of a cube are doubled the surface area is four times greater?
When the dimensions of a cube are doubled, each side length increases from ( s ) to ( 2s ). The surface area of a cube is calculated as ( 6s^2 ); therefore, the new surface area becomes ( 6(2s)^2 = 6 \times 4s^2 = 24s^2 ). This shows that the new surface area is four times greater than the original surface area of ( 6s^2 ). Hence, when the dimensions are doubled, the surface area indeed increases by a factor of four.
