Derivation of Formula for Area of Cyclic Quadrilateral
For a cyclic quadrilateral with given sides a, b, c, and d, the formula for the area is given by
Where s = (a + b + c + d)/2 known as the semi-perimeter.
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001 Solid steel ball remolded into hollow steel ball
Problem 001
A 523.6 cm3 solid spherical steel ball was melted and remolded into a hollow steel ball so that the hollow diameter is equal to the diameter of the original steel ball. Find the thickness of the hollow steel ball.
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001 A wire of given density and total mass
Problem 001
A certain wire that weighs 8.5 g/cc has a total mass of 155 kg.
- What is the density of the wire in kg/m3?
- Find the volume of the wire in cubic centimeter.
- If the total length of the wire is 1500 m, find the cross-sectional area in square millimeters.
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Derivation of Formula for Total Surface Area of the Sphere by Integration
The total surface area of the sphere is four times the area of great circle. To know more about great circle, see properties of a sphere. Given the radius r of the sphere, the total surface area is
Derivation of Formula for Volume of the Sphere by Integration
For detailed information about sphere, see the Solid Geometry entry, The Sphere.
The formula for the volume of the sphere is given by
Solution to Problem 696-697 | Beam Deflection by Method of Superposition
Problem 696
In Fig. P-696, determine the value of P for which the deflection under P will be zero.
Solution to Problem 694-695 | Beam Deflection by Method of Superposition
Problem 694
The frame shown in Fig. P-694 is of constant cross section and is perfectly restrained at its lower end. Compute the vertical deflection caused by the couple M.
Solution to Problem 693 | Beam Deflection by Method of Superposition
Problem 693
Determine the value of EIδ at the left end of the overhanging beam in Fig. P-693.
Solution to Problem 692 | Beam Deflection by Method of Superposition
Problem 692
Find the value of EIδ midway between the supports for the beam shown in Fig. P-692. (Hint: Combine Case No. 11 and one half of Case No. 8.)
Solution to Problem 691 | Beam Deflection by Method of Superposition
Problem 691
Determine the midspan deflection for the beam shown in Fig. P-691. (Hint: Apply Case No. 7 and integrate.)
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