SOLVE THE FF PROBLEMS. SHOW THE FIGURE & GIVE THE DETAILED SOLUTION. 1. The diameter of one sphere is three times that of another. What is the ratio of their areas? Of their volumes? 2. What is the radius of a sphere whose area and volume have the same numerical value? 3. If a ball 3 inches in diameter weighs 15 lb.’ what is the diameter of a ball of the same material weighing 120 lb. 4. A cylindrical jar 6 inches in diameter and 8 inches high, contains 50 spherical balls of 1 inch diameter. How many cubic inches of water must be added to fill the jar fully? 5. Find the volume of the largest sphere that can be submerged in a conical vessel of height 12 inches and radius 7 inches. 6. A pyramid of height 15 ft is to be divided into three solids by passing planes parallel to the base. Find the height of each solid if their volumes are equal.
Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
SOLVE THE FF PROBLEMS. SHOW THE FIGURE & GIVE THE DETAILED SOLUTION.
1. The diameter of one sphere is three times that of another. What is the ratio
of their areas? Of their volumes?
2. What is the radius of a sphere whose area and volume have the same
numerical value?
3. If a ball 3 inches in diameter weighs 15 lb.’ what is the diameter of a ball
of the same material weighing 120 lb.
4. A cylindrical jar 6 inches in diameter and 8 inches high, contains 50
spherical balls of 1 inch diameter. How many cubic inches of water must
be added to fill the jar fully?
5. Find the volume of the largest sphere that can be submerged in a conical
vessel of height 12 inches and radius 7 inches.
6. A pyramid of height 15 ft is to be divided into three solids by passing
planes parallel to the base. Find the height of each solid if their volumes
are equal.
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