# Video Discussion: MSTE-00 Problem Set 5

## Set 5 Part 1

- Find the volume of a circular cone having a base radius of 20 cm and axis 30 cm, if the axis makes an angle of 60° from the base.
- A sphere is circumscribing a cubical box having a volume of 8000 cm3. Compute the volume of the space between the cubical box and the sphere.
- A pole cast a shadow 15 m long when the angle of elevation of the sun is 61°. If the pole has lean 15° from the vertical directly towards the sun, what is the length of the pole?
- An airplane flew from Davao whose latitude is 14° N and longitude of 121° 30' E on a course of S 30° W and maintaining uniform altitude. At what longitude will the plane cross the equator?
- Determine the distance from point (2, 1) to the line $4x - 3y + 5 = 0$.

## Set 5 Part 2

- What is the length of the line with slope 4/3 from point (6, 4) to the
*y*-axis? - Find the equation of the radical axis of the two circles having equations of $x^2 + y^2 + 4x + 6y - 3 = 0$ and $x^2 + y^2 + 12x + 14y + 60 = 0$.
- Given $f(x) = (x - 4)(x + 3) + 4$. When $f(x)$ is divided by $x - k$, the remainder is $k$, find the value of $k$.
- The geometric mean and arithmetic mean of two numbers are respectively 8 and 17. Find the harmonic mean.
- In the CE Board examinations, the probability that an examinee will pass in each subject is 0.80. What is the probability that the examinee will pass at least two subjects.

## Set 5 Part 3

- The scale on the map is 1:
*n*. A square field has an area of 1600 sq. m. is represented by 1 cm^{2}, the value of*n*is: - If five masons can earn P675 in 6 days, how much can 12 carpenters receiving the same rate earn in 10 days?
*Situation.*Two flat belt pulleys have a center to center distance of 137 cm, and diameters of 72 cm and 36 cm, respectively. Neglecting the sagging of belt,- Compute the length of belt if both pulleys will rotate in the same direction.
- Compute the length of belt if the belt will be cross-connected to make the pulleys rotate in opposite directions.
- Determine the distance of the point from the center of the bigger pulley where the belt will cross when cross-connected.