Chapter 11 - Find the total area and volume of the following prisms.
1)
2)
3)
4)
Find the area of the base, total area, and volume of the following :
1. A rectangular prism with length 7 cm, width 6 cm, and height 2 cm.
2. A rectangular solid with length 3 m, width 1.2 m, and height .5 m.
3. Find the total area and volume of a cube with edge 5 cm.
4. Find the total area of a right hexagonal prism with height 12and base edges 3, 4, 5, 6, 5.2, and 6.3.
5. The total area of a cube is 216 cm2. Find the length of an edge. ______
6. The base of a right prism is a square with edge 4 cm. The volume is 64 cm3. Find the height. ______
Sketch the prism with base and height as described and find the total area and volume:
7. Triangle with sides 6,8,10; h = 12
8. Equilateral ∆ with side 6; h = 8
Cylinders For each cylinder or prism, find the area of the base, surface area andvolume
1. 2.
3. 4.
5. Find the total area of the toilet paper.6. Find the volume of the space between the cube and the cylinder.
7. Find the volume of the composite space figure.8. The surface area of a cylindrical septic tank is 290π ft2 and the radius is 5 ft. Find the height.
Find the following for a right cylinder.
9. r = 6, h = 8 B = ______T.A. = ______V= ______
10. r = 7, h = 24B = ______T.A. = ______V= ______
14. The lateral area of a cylinder is 100π. If r = 5, find h.
15. The total area of a cylinder is 144π. If r = h, find r.
16. Cylinder A has radius 4 and height 6. Cylinder B has radius 6 and height 4.
______a) which one has the greater lateral area?______a) which one has the greater volume?
Spheres
1.2. 3. 4.5. 6. 7.
Radius / 7 / 5 / ½ / k /Area / 64 / 324
Volume
9. Find the surface area and volume of a sphere with a radius of 5in. Leave your answer in terms of π.
10. The world’s largest disco ball has a diameter of 5.01m. Find the surface area and volume of the disco ball.
11. The circumference of a rubber ball is 13cm. Find the surface areato the nearest whole number.
Pyramids and Cones
Base -
Lateral faces -
Slant height –
Height/Altitude–
Find the total surface area and volume of the composite space figures.
7.1 Similar Figures
If 2 figures are similar then:
(1) CORRESPONDING ANGLES ARE ______(2) CORRESPONDING SIDES ARE ______
THE REDUCED RATIO OF 2 CORR. SIDES IS CALLED THE ______.
IF 2 FIGURES ARE SIMILAR, THEN THE RATIO OF THEIR ______IS = TO THE______.
SIMILARITY STATEMENT: Ex. ∆ BIG ~ ∆ MAN
1.) B ______I ___G ____
2)
Ex. 3
∆GWT ~ ∆ GIH
Scale Factor:
Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement. If not, explain why not.
1.2.
3.parallelograms EFGH and TUVW4.CDE and LMN
Tell whether the polygons must be similar based on the information given in the figures.
5..
7.8.
7.3 Identifying Similar Triangles
Angle-Angle Similarity Postulate (AA~) If two angles are congruent to two angles of another triangle, then the triangles are similar.
Side-Side-Side Similarity Theorem (SSS~)If the measures of the corresponding sides of two triangles are proportional, then the triangles are similar.
Side-Angle-Side Similarity Theorem (SAS~) If the measures of two pair of corresponding sides of two triangles are proportional and the included angle is congruent, then the triangles are similar.
Determine whether each pair of triangles is similar. If so, state whether it
is similar by AA~, SSS~ or SAS~.
1) 2)
______
3) 4)
5) 6)
Find x and y in each shape.
7) 8)
PRACTICE PROBLEMSWrite a similarity statement . Explain why the triangles are similar (AA~, SAS~, SSS~)
1.2.3.
CAT ~ SNA ~______DOR ~______
Reason: Reason: Reason:
Solve for the missing sides.
4.5.6.
x = ______a = ______x = ______
y = ______b = ______y = ______
z = ______c = ______z = ______
7.4 Triangle Proportions
Theorem: If a line is parallel to one side of a ∆ and intersects the other two sides, then it
______.
Ex. Given:
Conclusion: ______
And C ______; AEB ______
Ex. Given:
Ex 1. If AB = 1, BC = 3, and AE = 2.5, find ED.
Ex. 2 If AB = 6, BC = 10, and AD = 14, find AE.
Theorem: On any 2 transversals, parallel lines
______.
Given: Lines l // m // k
Conclusion: ______
Ex. 1: If a = 5 , b = 7, and d = 9, find c.
Ex. 2: If a = 2, b = 3, and c + d = 20, find d.
∆ Angle Bisector Theorem:
If a ray bisects an of a ∆, then it divides the opposite side into segments
proportional to ______.
Given: bisects ABC in ∆ABC. Conclusion: ______
Use diagram above:
Ex. 1 If BA = 12, BC = 24, and AD = 10, find AC.
Ex. 2: If BA = x, BC = 8, DA = 2 and DC = 7, find x.
Ex. 3 Find the value of x in the diagram to the right:
Find each length.
1.BH______2.MV______
1