March 2021

A circle 8 cm in radius is tangent to a line at A. Another circle 3 cm in radius is tangent also to the same line at B. Find the distance AB if the two circles are tangent externally to each other.

A hole 10 inches in diameter is to be punched out from a sphere having a diameter of 16 inches. Determine the volume punched out if the center of the hole is along the diameter of the sphere.

A boy is 25 years younger than his father. In 10 years, his father will be twice his age. Find the age of the boy.

Two regular pentagons are concentric to each other. One of which has sides of 20 m and the other has sides of 10 m. If their corresponding vertices are in the same direction, find the area inside the larger pentagon but outside the smaller pentagon.

The area bounded by the waterline of a reservoir is determined by using planimeter and the following are the results: A₁ = 20,000 m²; A₂ = 18,000 m²; A₃ = 14,000 m²; A₄ = 10,000 m²; and A₅ = 8,000 m². If the contour interval is 2 m, find the capacity of the reservoir (in cubic meter) using end area method.

A non-square rectangle is inscribed in a square so that each vertex of the rectangle is at the trisection point of the different sides of the square. Find the ratio of the area of the rectangle to the area of the square.

A trapezoid has an area of 360 m² and altitude of 20 m. Its two bases have ratio of 4:5. One of the bases i

The magnetic bearing of a line was recorded as S 80° 15' W in 2000 at Mactan Island which had a declination of 16° E in that year. Compute the present magnetic bearing of the same line in 2006 if the declination in 2006 is 4° 30' E.

A slope of 20 degrees in percent is most nearly equal to:

A cube is 6 inches in edge. A cutting plane is passed through the midpoint of three adjacent edges. Find the volume of the smaller solid.