Chapter 10 Sample Problems

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1. Surface area is measured in units of this type.

a). linear units c). cubic units
b). square units d). fractional units

___________

2. Volume is measured in units of this type.

a). square units c). linear units
b). cubic units d). neither a, b, or c

___________

3. A polyhedron with 6 vertices and 12 edges will have how many faces?

a). 18 c). 4
b). 8 d). 14

___________

4. Which of the following is not a regular polyhedron.

a). tetrahedron c). octahedron
b). cuboctahedron d). icosahedron

___________

5. A drawing which shows three sides of an object from a corner view.

a). foundation c). orthographic
b). isometric d). cross section

___________

6. A drawing which shows the base of an object.

a). foundation c). orthographic
b). isometric d). cross section

___________

7. A drawing which shows the top, front, and right-side views of an object.

a). foundation c). orthographic
b). isometric d). cross section

___________

8. A two-dimensional pattern you can fold to form a three-dimensional figure.

a). cross section c). net
b). polygon d). polyhedron

___________

9. How may "semi-regular" Archimedean solids are there?

a). five c). ten
b). twenty d). thirteen

___________

10. A prism is a polyhedron that has two parallel, congruent faces called

a). lateral faces c). bases
b). sides d). polygons

___________

11. What is the correct formula for the surface area of a right prism?

a). 2B + ph c). 2B + Ch
b). B + 1/2(pl) d). B + ph

___________

12. A solid with congruent circular bases that lie in parallel planes

a). cylinder c). cone
b). sphere d). frustum

___________

13. In a prism, the lateral faces are of this shape

a). squares c). parallelograms
b). regular polygons d). pyramids

___________

14. In a right cone, the name given the distance between the vertex and a point on the edge of the base.

a). altitude c). slant height
b). height d). radius

___________

15. The set of all points in space that are a given distance, r, from a point called the center.

a). radius c). circle
b). chord d). sphere

___________

16. Two similar pyramids have altitudes of 12 and 42 inches respectively. If the volume of the first pyramid is 324 in³, what is the volume of the second pyramid?.



Vol. = __________ in³

17. The diameter of a sphere is 36 inches. What is the surface area and volume of the sphere?



Surface Area = __________ in²
Vol. = __________ in³

18. Two spheres have radii in a ratio of 2:5. If the volume of the first sphere is 904.778684 cm³, what is the surface area and volume of the second sphere?



Surface Area = __________ cm²
Vol. = __________ cm³

19. Find the indicated values for the prism.

     Prism

Base Area = ____________ cm²
Lateral Area = ____________ cm²
Total Surface Area = ____________ cm²
Volume = ____________ cm³


20. Find the indicated values for the pyramid.

     Pyramid

Base Area = ____________ cm²
Lateral Area = ____________ cm²
Total Surface Area = ____________ cm²
Volume = ____________ cm³


21. Find the indicated values for the prism.

     Prism

Base Area = ____________ cm²
Lateral Area = ____________ cm²
Total Surface Area = ____________ cm²
Volume = ____________ cm³


22. Find the indicated values for the cone.

     Cone

Base Area = ____________ in²
Lateral Area = ____________ in²
Total Surface Area = ____________ in²
Volume = ____________ in³


23. Find the indicated values for the cylinder.

     Cylinder

Base Area = ____________ in²
Lateral Area = ____________ in²
Total Surface Area = ____________ in²
Volume = ____________ in³


24. Find the indicated values for the prism.

     Prism

Base Area = ____________ cm²
Lateral Area = ____________ cm²
Total Surface Area = ____________ cm²
Volume = ____________ cm³


25. Find the indicated values for the prism.

     Prism

Base Area = ____________ in²
Lateral Area = ____________ in²
Total Surface Area = ____________ in²
Volume = ____________ in³


26. Find the indicated values for the cylinder.

     Cylinder

Base Area = ____________ cm²
Lateral Area = ____________ cm²
Total Surface Area = ____________ cm²
Volume = ____________ cm³


27. Find the indicated values for the prism with a cylindrical hole. The cylinder has a radius of 6 cm.

     Prism with cylindical hole

Base Area = ____________ cm²
Lateral Area = ____________ cm²
Total Surface Area = ____________ cm²
Volume = ____________ cm³


28. Find the indicated values for the prism with a pyramidal top.

     Prism with pyramidal top

Base Area = ____________ cm²
Lateral Area = ____________ cm²
Total Surface Area = ____________ cm²
Volume = ____________ cm³


29. Water is pouring into a conical (cone-shaped) reservoir at the rate of 1.8 m³ per minute. Determine the number of minutes it will take to fill the reservoir.

     Conical reservoir

Time = __________ min


30. The purple shaded pyramid in the diagram is cut from the gray rectangular solid. How does the volume of the pyramid compare with the volume of the rectangular solid?

     Rectangular Solid

Vol Pyramid/Vol Rect. Solid = ____________



31. The container shown has the shape of a rectangular solid. When the rock is submerged in the water, the water level rises 0.5 cm. Find the volume of the rock.

     Rectangular Solid

Vol. of Rock = ____________ cm³


32. A driveway 30 meters long and 5 meters wide is to be paved with blacktop 3 cm thick. How much will the blacktop cost if it is sold at the price of $175.00 per meter³?

 

 

Cost = $__________

33. A diagonal of a box forms a 35° angle with a diagonal of the base. Use trigonometry to approximate the volume of the box.

     Rectangular Solid

 

Vol. of Box = ____________ cm³

34. A solid metal cylinder with a radius of 6 cm and a height of 18 cm is melted down and recast as a solid cone with a radius of 9 cm. Find the height of the cone.

 

 

Height = __________ cm

35. A hemispheric bowl with a radius of 25 cm contains water whose depth is 10 cm. What is the water’s surface area?

     Hemispheric Bowl

 

Surface Area of the Water = ____________ cm²

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