Solid Geometry - ISEE Middle Level Quantitative Reasoning
Card 0 of 2
Which is the greater quantity?
(a) The sidelength of a cube with surface area 
(b) The sidelength of a cube with volume 
Which is the greater quantity?
(a) The sidelength of a cube with surface area
(b) The sidelength of a cube with volume
(a) A cube has six faces, each a square. Since the surface area of this cube is 
, each face has one-sixth this area, or 
; the sidelength is the square root of this, or 
.
(b) The volume of a cube is the cube of its sidelength, so we take the cube root of the volume of this cube to get the sidelength:
The cubes have the same sidelength.
(a) A cube has six faces, each a square. Since the surface area of this cube is
(b) The volume of a cube is the cube of its sidelength, so we take the cube root of the volume of this cube to get the sidelength:
The cubes have the same sidelength.
Compare your answer with the correct one above
Which is the greater quantity?
(a) The volume of a rectangular prism with length 60 centimeters, width 30 centimeters, and height 15 centimeters
(b) The volume of a cube with sidelength 300 millimeters
Which is the greater quantity?
(a) The volume of a rectangular prism with length 60 centimeters, width 30 centimeters, and height 15 centimeters
(b) The volume of a cube with sidelength 300 millimeters
(a) The volume of the prism is the product of its length, its width, and its height:
(b) The volume of the cube is the cube of its sidelength. We restate 300 millimeters as 30 centimeters, and cube this:
The volumes are equal.
(a) The volume of the prism is the product of its length, its width, and its height:
(b) The volume of the cube is the cube of its sidelength. We restate 300 millimeters as 30 centimeters, and cube this:
The volumes are equal.
Compare your answer with the correct one above