The Cylinder

Cylinder is a solid bounded by a closed cylindrical surface and two parallel planes.
 

Common Prisms: Cube and Rectangular Parallelepiped

There are two very common prisms; the cube and rectangular parallelepiped. In non-mathematical term, both are called box.
 

The Prism

Prism is a polyhedron in which two faces are equal polygons in parallel planes, and all other faces are parallelograms. There are two types of prism; oblique prism and right prism. Oblique prism is when the axis is not perpendicular to the base and right prism if the axis is parallel to the base. In right prism, all lateral areas are rectangle.
 

Solids for which Volume = Area of base times Altitude

Solids in which V = Ab × h
This is a group of solids in which the volume is equal to the product of the area of the base and the altitude. Two types of solids belong to this group namely, prisms and cylinders.
 

Trapezoidal Strip of Land from a Triangular Lot

Problem
A strip of 640 m2 is sold from a triangular field whose sides are 96 m, 72 m, and 80 m. The strip is of uniform width h and has one of its sides parallel to the longest side of the field. Find the width of the strip.

A. 7.1 m
B. 8.1 m
C. 8.7 m
D. 7.7 m
 

004 Components of a 3D force with given angles

Problem 004
Referring to Fig. 1.4, determine the angle between vector A and the y-axis.
A. 65.7°
B. 73.1°
C. 67.5°
D. 71.3°
 

Force with given angle from z-axis

 

003 Components of a 3D force with given distances

Problem 003
Which of the following correctly defines the 500 N force that passes from A(4, 0, 3) to B(0, 6, 0)?
A. 256i - 384j + 192k N
B. -256i + 384j - 192k N
C. -384i + 192j - 256k N
D. 384i - 192j + 256k N
 

Example 001 | Sum and Difference of Two Angles

Problem
If tan x = 1/3 and tan y = 1/2, what is the value of tan (x + y) and tan (x - y)?
 

002 Components of forces with given slope

Problem 002
Compute the x and y components of each of the four forces shown in Fig. P-002.
 

001 Horizontal and vertical componets of planar forces

Problem 001
Problem Determine the x and y components of the forces shown below in Fig P-001.
 

Components of Forces in XY Plane

 

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