Edges and diagonals of cuboids

Edge length of a cube from its volume ●○○○○ 10 ptsThe volume of a cube is $3\frac{3}{8}$ cubic inches. Find the length of each edge of the cube in inches. Give your answer as a decimal.
Height of a cuboid from its edges ●○○○○ 10 ptsA cuboid has a base measuring 8 cm by 10 cm. The total length of all its edges is 92 cm. Find the height of the cuboid in centimetres.
Side of a cube with volume 112 ●○○○○ 10 ptsThe volume of a cube is 112 cubic units. Find the length of each side. Round to two decimal places.
Product of cube diagonal lengths ●●○○○ 20 ptsA cube has side length 1. Find the product of the lengths of the diagonals of this cube, where a diagonal is a line segment between two vertices that is not an edge.
Surface area from edge sum and diagonal ●●○○○ 20 ptsThe sum of the lengths of the twelve edges of a rectangular box is $140$ , and the distance from one corner of the box to the farthest corner is $21$ . What is the total surface area of the box?
Cube volume equals six times edge sum ●●○○○ 20 ptsThe volume of a cube is numerically equal to six times the sum of the lengths of its edges. Find the volume of the cube, in cubic units, rounded to two decimal places.
Edge length of a cube from distances ●●●○○ 50 ptsLet $P$ be a point inside the cube $ABCD\text{-}EFGH$ , where $ABCD$ and $EFGH$ are opposite faces and $E,F,G,H$ lie directly above $A,B,C,D$ respectively. Given $PA=PB=\frac{3\sqrt{3}}{2}$ and $PF=PC=\frac{\sqrt{107}}{2}$ , find the edge length of the cube.
Longest edge of a rectangular block ●●●○○ 50 ptsThe lengths of three unequal edges of a rectangular solid block are in geometric progression. The volume of the block is $216\ \text{cm}^3$ and its total surface area is $252\ \text{cm}^2$ . Find the length of the longest edge, in cm.

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