Midterm Exam

Question 1

The volume of water in a hemispherical tank is 687 cm3. If the radius of the hemispherical bowl is 15 cm, find the depth of the tank in cm.

Answer 1

4.5 cm

Question 2

Melissa can mow the lawn in 4 hours, while her husband, George can mow the lawn in 3 hours. They agreed to mow the lawn together. How long will it take them to mow the lawn together?

Answer 2

1.7 hours

Question 3

Find the area which is inside the circle r = 3 sin ϴ and outside the cardioid r = 1 + sin ϴ.

Answer 3

π sq. units

Question 4

A right pyramid has a hexagon base with sides 12 cm each. The lateral edge of the pyramid measures 28 cm. Find the lateral area of the pyramid.

Answer 4

984.60 cm²

Question 5

Find the distance between the parallel lines 3x - 4y + 4 = 0 and 3x - 4y - 16 = 0.

Answer 5

4

Question 6

A pyramid having an altitude of h is divided into 3 parts by 2 planes passed parallel to the base. These planes are at distances of h/3 and (2/3)h from the base. Determine the volume of the middle part if the volume of the pyramid is 180 cm³.

Answer 6

46.67 cm³

Question 7

Find the closest distance from the point ( 1, 4 ) to the parabola y² = 2x.

Answer 7

2.34

Question 8

Standard sign shape for STOP sign.

Answer 8

octagon

Question 9

The parabola y = x² + C has the line y = 2x + 4 as its tangent. Find the value of C.

Answer 9

5