Computation Quiz

A solid metal ball is immersed in a pail of paint and displaces 288π cm3 of paint. What is the total area painted?

• 72π

• 112π

• 136π

• 144π

In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions?

• 720 ways

• 120 ways

• 36 ways

• 20 ways

In two regular polygons with the same number of sides, find the length of a side of the smaller if the lengths of apothems are 20 and 50 and a side of the larger has length 32.5.

• 13

• 14

• 15

• 16

Mines in a harbor during wartime are so placed that ship going to a certain port within the harbor, to avoid hitting them must follow a path which is at all times equidistant from a point 9 km north of another port and a line whose bearing is due east. One point of this line is 3 km south of the port. Considering the port as the origin, find the equation of the path of the ship.

• x2 + 24y + 72 = 0

• x2 - 24y + 72 = 0

• x2 - 24y - 72 = 0

• x2 + 24y - 72 = 0

If the sum of the angles A + B + C = 180° and tan A + tan B + tan C = x, find the equivalent value of (tan A) (tan B) (tan C).

• x

• sqrt x

• x/2

• 1 - x

A rectangular prism of metal having dimensions 4.3 cm by 7.2 cm by 12.4 cm is melted down and recast into a frustum of a square pyramid, 10% of the metal being lost in the process. If the ends of the frustum are squares of side 3 cm and 8 cm respectively, find the thickness of the frustum.

• 12.87 cm

• 11.87 cm

• 10.69 cm

• 9.43 cm

A quadrilateral ABCD is inscribed in a circle. The angle ADC = 75° and angle ACD = 45°. If the arc BC is only one-half of arc CD, find the value of angle BCA.

• 30°

• 45°

• 50°

• 60°

Given a circle of radius 4 and center at (6,8). Find the locus of the center of all circles that is tangent to the x-axis and the given circle.

• x2−12x−24y+84=0

• x2+12x−24y−60=0

• x2+12x+24y−156=0

• x2−12x+24y−12=0

In hilly or mountainous terrain, it is often difficult to determine heights. It may be impossible to find an expanse of level ground from which measurements can be taken, and sighting may be limited. Mountain peaks may be visible only from certain places. A geologist took at two points, B and C, 928 m apart. The angle of elevation from B to the top of the mountain at A is 47°10'. The angle of elevation from C to B is 8°40', and the angle of elevation from C to A is 32°30'. It is known that the elevation at C is 1621 m to the nearest meter, what is the elevation at A?

• 2921 m

• 2524 m

• 283 m

• 2847 m

The probabilities that three men hit a target are 1/6, ¼, and 1/3, respectively. Each shoot once at a target. If only one of them hits the target, find the probability that it was the first man?

• 1/12

• 6/31

• 31/72

• 5/36