Area, Perimeter, and Volume - GRE Quantitative Reasoning

$C=2\pi r$. Represents the total length around the circle as twice pi times the radius.

$A=\pi r^2$. Calculates the space inside the circle using pi times the square of the radius.

$A=bh$. Multiplies base by perpendicular height to find the enclosed area, regardless of side angles.

$A=\frac{1}{2}(b_1+b_2)h$. Averages the two bases and multiplies by height to account for the trapezoid's shape.

$A=\frac{1}{2}d_1d_2$. Uses half the product of the diagonals, as they bisect the rhombus or kite into four right triangles.

$V=lwh$. Multiplies the three dimensions to determine the space occupied by the rectangular solid.

$SA=2(lw+lh+wh)$. Sums the areas of all six faces by doubling the products of each pair of dimensions.

$V=\pi r^2h$. Multiplies the circular base area by the height to find the cylinder's volume.

$SA=2\pi r^2+2\pi rh$. Adds the areas of two bases and the lateral surface, which unwraps to a rectangle of width $2\pi r$ and height $h$.

$V=\frac{1}{3}\pi r^2h$. Takes one-third of the cylinder's volume with the same base and height due to the cone's tapering shape.

$V=\frac{4}{3}\pi r^3$. Derives from integrating cross-sectional areas, resulting in four-thirds pi times radius cubed.

$SA=4\pi r^2$. Represents the total surface as four times the area of a great circle of the sphere.

$V=Bh$. Multiplies the base area by the height to fill the prism's cross-sectional shape along its length.

$V=\frac{1}{3}Bh$. Uses one-third of the prism's volume with the same base and height due to the pyramid's apex convergence.

$P=4s$. Multiplies the side length by four since all sides of the square are equal.

$A=s^2$. Squares the side length to compute the area enclosed by the square.

$A=lw$. Multiplies length by width to calculate the total space enclosed by the rectangle.

$A=\frac{1}{2}bh$. Takes half the product of base and height since the area is half of a parallelogram with the same base and height.

$A=\frac{1}{2}\pi r^2$. Halves the full circle's area since a semicircle covers half the space without including the diameter's contribution.

$A=21$. Applies the rectangle area formula by multiplying length 7 by width 3.

Volume is multiplied by $k^3$. Scales with the cube of linear dimensions, multiplying volume by $k^3$.

Area is multiplied by $k^2$. Scales with the square of linear dimensions, multiplying area by $k^2$.

Perimeter is multiplied by $k$. Scales linearly with the dimensions, so perimeter increases by the factor $k$.

$V=20\pi$. Computes using the cylinder volume formula with base area $\pi (2)^2$ times height 5.