
Find the total surface area and the volume of a closed cylindrical container with radius 5 cm and a height of 34 cm.
Solution
The total surface area A of a cylinder is given by the sum of the area of the lateral surface plus the areas of the base and bottom of the container.
A = 2 × radius × Pi × height + Pi × radius^{2} + Pi × radius^{2}
= 2 × 5 × Pi × 34 + 3.14 × 5^{2} + Pi × 5^{2}
= 340 Pi + 25 Pi + 25 Pi = 390 Pi square centimeters
= 1224.6 square centimeters
The volume V of the given cylinder is equal to
V = Pi × radius^{2} × height
= Pi × 25 × 34 = 850 Pi cubic centimeters
= 2669 cubic centimeters (using Pi = 3.14)

Find the total surface area and the volume of a closed conical container with radius 5 cm and a height of 15 cm.(round your answer to the nearest unit.)
Solution
The total surface area A of a cone is given by the sum of the area of the lateral surface plus the area of the base.
A = Pi × radius × slant height + Pi × radius^{2}
The slant height S, the height of the cone (h = 15 cm) and the radius (r = 5 cm) of its base form a right triangle where S may be found using Pythagor's theorem as follows.
S^{2} = 15^{2} + 5^{2} = 250
S = 15.8 cm
A = Pi × 5 × 15.8 + Pi × 25
= 104 Pi square centimeters
= 327 square centimeters (using Pi = 3.14)
The volume V of the cone is given by.
V = (1/3) × Pi × r^{2} × h
= (1/3) × Pi × 5^{2} × 15
= 125 Pi cubic centimeters
= 393 cubic centimeters

A cube has a total surface area of the six faces equal to 150 square feet. What is the volume of the cube?
Solution
The surface area of one square face is equal to
150 / 6 = 25 square feet
Since the face of a cube is square, if x is the length of an edge of the cube, then
x^{2} = 25 square feet
and x = 5 feet
The volume V of the cube is equal to
V = 5 × 5 × 5 = 125 cubic feet

Which two angles are complementary?
 21 degrees and 78 degrees
 58 degrees and 22 degrees
 67 degrees and 23 degrees
 140 degrees and 40 degrees
Solution
Two angles are complementary if the sum of their measures is equal to 90°
 21 ° + 78 ° = 99 °
 58 ° + 22 ° = 80 °
 67 ° + 23 ° = 90 °
 140 ° + 40 ° = 180 °
Angles 67 ° and 23 ° are complementary

Which two angles are not supplementary?
 30 degrees and 150 degrees
 5 degrees and 175 degrees
 89 degrees and 91 degrees
 23 degrees and 177 degrees
Solution
Two angles are supplementary if the sum of their measures is equal to 180°
 30 ° + 150 ° = 180 °
 5 ° + 175 ° = 180 °
 89 ° + 91 ° = 180 °
 23 ° + 177 ° = 200 °
Angles 23 ° and 177 ° are not supplementary.

Find the height h of the trapezoid so that its area is equal to 400 square cm.
.
Solution
The area A of a trapezoid is given by the formula
A = (1/2)(base1 + base2) × height
= (1/2)(27 + 13) × h
The area A of the trapezoid is equal to 400 square cm. Hence
(1/2)(27 + 13) × h = 400
(1/2)(40) × h = 400
20 × h = 400
h = 20 cm

Find the width w of the parallelogram so that its area is equal to 600 square feet.
.
Solution
The area A of a parallelogram is equal to
A = W × height = W × 20 = 600
W = 600 / 20 = 30 feet

Find area of the shaded shape.
.
Solution
The shaded (blue) shape is made up of a large rectangle of length 40 and width 25 from which a smaller rectangle (left) of width 14 and width 12 and a triangle (right) of base 25 and height 10 have been cut. Hence the area of this shape is equal to
Area of large rectangle  area of smaller rectangle  area of triangle
= 40 × 25  14 × 12  (1/2) × 25 × 10 = 707 square cm

Find the total surface area of the box open at the top.
.
br>
Solution
Area of the open box is equal to
The areas of the front and back faces + the areas of the left and right faces + the area ot bottom
= 2(12 × 11) + 2(9 × 11) + 9 × 12 = 570 square cm

If the quadrilateral ABCD is a parallelogram, what are the coordinates of point D?
.
Solution
Since ABCD is a parallelogram sides AB and DC are parallel. Because points A and B have the same y coordinate, AB is parallel to the x axis. Hence DC is also parallel to the x axis and therefore the y coordinate of point D is the same as the y coordinate of C and is equal to 2. Also distance AB must be equal to distance CD. Hence if a is the x coordinate of C, then
7  a = 8  2
x = 1
Point C has coordinates (1 , 2)

Which of these are right triangles?
.

Find x if triangle ABC is a right triangle.
.

Find all the unknown sides x, y, z and w if all three triangles are similar.
.

A quadrilateral with vertices (2,6) , (6,8) , (9,2) and (4,1) is reflected on the x axis. What are the coordinates of the vertices of the quadrilateral after reflection?

The side of cube A is 3 times the side of cube B. The volume of cube A is 3,375 cubic feet. Find the volume of cube B.

The length of rectangle A is 24 cm and the length of rectangle B is 96 cm. The two rectangles are similar. Find the ratio of the area of A to the area of B.
Answers to the Above Questions
 area = 390 pi square cm , volume = 850 pi cubic cm
 area = 327 square cm , volume = 393 cubic cm
 volume = 125 cubic feet
 C) 67 degrees and 23 degrees are complementary
 D) 23 degrees and 177 degrees are not supplementary
 h = 20 cm
 w = 30 feet
 area = 707 square cm
 surface area = 570 square cm
 (1 , 2)
 triangles A) and C) are right triangles

x = 102 ^{o}
 x = 9 , y = 51 , z = 144 , w = 36
 vertices after reflection (2,6) , (6,8) , (9,2) and (4,1)
 volume of cube B = 125 cubic feet
 ratio of area of A to area of B = 1:16

