SOLID GEOMETRY DONE BY: ABDELAZIZ HUSAIN ALI GRADE: 12-02

WHAT IS SOLID GEOMETRY? In mathematics, solid geometry was the traditional name for the geometry of three-dimensional Euclidean space — for practical purposes the kind of space we live in. Geometry deals with the measurements of volumes of various solid figures including cylinder, circular cone, truncated cone, sphere, and prisms.

ABOUT SOLID GEOMETRY It is called three-dimensional, or 3D because there are three dimensions: width, depth and height. DEPTH HEIGHT WIDTH

SIMPLE SHAPES Some of the simplest shapes:

PROPERTIES OF SOLID GEOMETRY Volume (think of how much water it could hold). Surface area (think of the area you would have to paint). How many vertices (corner points), faces and edges they have.

SAT QUESTIONS ABOUT SOLID GEOMETRY

1) A cubic box has sides of length x. Another cubic box has sides of length 4x. How many of the boxes with length x could fit in one of the larger boxes with side length 4x? A.80 B.64 C.40 D.16 E.4

EXPLANATION The volume of a cubic box is given by (side length) 3. Thus, the volume of the larger box is 4x 3 = 64x 3, while the volume of the smaller box is x 3. Divide the volume of the larger box by that of the smaller box, 64x 3 / x 3 =64.

2) I have a hollow cube with 3 inch per side suspended inside a larger cube of 9 inch per side. If I fill the larger cube with water and the hollow cube remains empty yet suspended inside, what volume of water was used to fill the larger cube? A.73in 3 B.72in 3 C.702in 3 D.912in 3 E.698in 3

EXPLANATION Determine the volume of both cubes and then subtract the smaller from the larger. The large cube volume is 9×9×9=729in 3 and the small cube is3×3×3=27in 3. The difference is 702 in 3.

3) If the volume of a cube is 50ft3, what is the volume when the sides double in length? A.500ft 3 B.200ft 3 C.300ft 3 D.400ft 3 E.600ft 3

EXPLANATION Using S as the side length in the original cube, the original is S×S×S. Doubling one side and tripling the other gives 2S×2S×2S for a new volume formula for 8S×S×S, showing that the new volume is 8× greater than the original.

4) A spherical orange fits snugly inside a small cubical box such that each of the six walls of the box just barely touches the surface of the orange. If the volume of the box is 64in 3, what is the surface area of the orange in square inches? A.64π in 2 B.256π in 2 C.128π in 2 D.32π in 2 E.16π in 2

EXPLANATION The volume of a cube is found by V= s 3. Since V = 64, s = 4. The side of the cube is the same as the diameter of the sphere. Since d = 4, r = 2. The surface area of a sphere is found by SA = 4πr 2 = 4π2 2 = 16π in 2.

5) A cylinder has a volume of 20 in 3. If the radius doubles, what is the new volume? A.80 in3 B.40 in3 C.100 in3 D.60 in3 E.50 in3

EXPLANATION The equation for the volume of the cylinder is πr 2 h. When the radius doubles (r becomes 2r) You get π(2r) 2 h = 4πr 2 h. So when the radius doubles, the volume quadruples, giving a new volume of 80 in 3.

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