Module 05: Plane and Solid Geometry – Mechanical Engineering Online Review Center

Handouts
Exercises

LINK: Plane and Solid Geometry

Topics:

Triangle
Rectangle
Square
Quadrilaterals
Regular Polygons
Circle
Ellipse
Polyhedron

Find the area of a pentagon having a perimeter of 60-in.
- a. 234.8 in²
- b. 247.7 in²
- c. 220.2 in²
- d. 212.7 in²
If the numbers of diagonals in a polygon is 9, what is the description of the polygon?
- a. Hexagon
- b. Nonagon
- c. Pentagon
- d. Decagon
The area of a circle is 160 in², what is the length of a side of regular hexagon inscribed in this circle?
- a. 5 in
- b. 6 in
- c. 8 in
- d. 7 in
What is the largest diameter of a circle that will fit inside a regular pentagon with 5-in sides.
- a. 6.9 in
- b. 5.3 in
- c. 7.8 in
- d. 8.1 in
How many diagonals are there in a polygon of 18 sides?
- a. 130
- b. 125
- c. 135
- d. 140
A heptagon is circumscribed in a circle whose area is 160 cm2. Determine the length of side of heptagon.
- a. 5.3 cm
- b. 7.2 cm
- c. 6.9 cm
- d. 8.3 cm
A hexagon has an apothem of 6-in. Find the length of side of the polygon.
- a. 8.3 in
- b. 5.3 in
- c. 6.9 in
- d. 7.2 in
The sum of interior angle of nonagon is _____.
- a. 1360 deg
- b. 1260 deg
- c. 1420 deg
- d. 1800 deg
Find the interior angle of a decagon _____.
- a. 360 deg
- b. 180 deg
- c. 165 deg
- d. 144 deg
What is the radius of a circle inscribed in a triangle with sides of 7, 10 and 14-in?
- a. 2 in
- b. 3 in
- c. 4 in
- d. 5 in
A trapezoid has a bottom base of 12-in and top base of 7-in. If the height is 6-in, find the area.
- a. 57 in²
- b. 60 in²
- c. 55 in²
- d. 52 in²
Find the length of side of an equilateral triangle whose area is equal to 420-in².
- a. 28.2 in
- b. 34.1 in
- c. 38.9 in
- d. 31.1 in
A rectangle has a width of 12 m and area of 100 m². If the perimeter of rectangle is equal to the perimeter of equilateral triangle, find the area of equilateral triangle.
- a. 65.2 m²
- b. 79.6 m²
- c. 74.3 m²
- d. 67.3 m²
The area of a circle is 310-in². What is the circumference?
- a. 58.2 in
- b. 73.1 in
- c. 62.4 in
- d. 68.9 in
The area of a circle is 260-in². What is the diameter of the circle?
- a. 16.3 in
- b. 18.2 in
- c. 20.6 in
- d. 14.3 in
What is the area of an ellipse with an aspect ratio of 2.5 and total perimeter of 28-inches?
- a. 50.8 in²
- b. 45.3 in²
- c. 48.2 in²
- d. 43.0 in²
A rhombus has diagonals of 34 and 25-inches. Find the area.
- a. 425 in²
- b. 428 in²
- c. 433 in²
- d. 430 in²
The area of a triangle inscribed in a circle is 40 cm2 and the radius of the circumscribed circle is 8.15 cm. If the two sides of the inscribed triangle are 9 cm and 12 cm, respectively, calculate the third side.
- a. 10 cm
- b. 12 cm
- c. 14 cm
- d. 16 cm
The sides of a triangle are 10 cm, 12 cm and 16 cm. Find the radius of the inscribed circle.
- a. 2.18 cm
- b. 3.15 cm
- c. 4.00 cm
- d. 5.23 cm
A square has a diagonal of 18 inches. Find the length of its sides.
- a. 10.8 in
- b. 11.5 in
- c. 13.4 in
- d. 12.7 in
A rectangular lot has a width of 16 m and length of 25 m. Find the diameter of a circular lot whose area is twice that of rectangular lot.
- a. 28.1 m
- b. 34.3 m
- c. 25.3 m
- d. 31.9 m
Find the area of equilateral triangle whose sides is 12-in.
- a. 62.4 in²
- b. 64.3 in²
- c. 66.2 in²
- d. 68.5 in²
In triangle ABD, A=35^o, B=82^o and b=12-in. Find the area of the triangle.
- a. 28.3 in²
- b. 25.8 in²
- c. 34.3 in²
- d. 38.8 in²
Find the area of triangle whose sides are 32 cm, 37 cm and 48 cm.
- a. 560.3 cm²
- b. 591.6 cm²
- c. 538.2 cm²
- d. 521.8 cm²
Find the area of circle inscribed in a square whose area is 250-in².
- a. 190.3 in²
- b. 200.0 in²
- c. 196.3 in²
- d. 193.8 in²
A large 25 m diameter cylindrical tank that sits on the ground is to be painted. If one liter of paint covers 12 m2, how many liters are required if it is 12 m high (include the top).
- a. 119.5 L
- b. 123.5 L
- c. 128.5 L
- d. 130.5 L
A square has a perimeter of 60-in. If the area of square is equal to the circle, determine the circumference of the circle.
- a. 50 in
- b. 58 in
- c. 55 in
- d. 53 in
A closed cylinder has a height of 4 m and diameter of 8 m. Find the inner surface area.
- a. 180 m²
- b. 192 m²
- c. 198 m²
- d. 200 m²
A pyramid has a rectangular base of 12 in x 14 in. If the height is 16-in, find the volume of pyramid.
- a. 800 in³
- b. 880 in³
- c. 885 in³
- d. 896 in³
A spherical water tank 12 m diameter is filled to a height of 3/2 of its radius. Find the volume of water in the tank.
- a. 750 m³
- b. 765 m³
- c. 785 m³
- d. 763 m³
A steel plate made of 1.5-in x 5 ft x 12 ft has a density of 0.285 lb/in³. Find the weight of the material.
- a. 3693.6 lbs
- b. 3505.2 lbs
- c. 3400.1 lbs
- d. 3720.8 lbs
A cylindrical truncated prism has a base diameter of 12 m. The shortest height is 6 m and the longest height is 12 m, find the volume of the prism.
- a. 1038.2 m³
- b. 1128.9 m³
- c. 1017.9 m³
- d. 1213.7 m³
A cube has a diagonal of 6 ft, determine the diameter of a sphere whose volume is thrice that of the cube.
- a. 6.20 ft
- b. 3.01 ft
- c. 8.32 ft
- d. 4.30 ft
A sphere whose diameter increases from 5 cm to 7 cm? What is the percent increase in the surface area.
- a. 90%
- b. 96%
- c. 93%
- d. 98%
What is the total surface are including the base, of a 7 foot high right circular cone with a 5 feet base?
- a. 75.3 ft²
- b. 82.1 ft²
- c. 78.5 ft²
- d. 80.1 ft²

Answer Key (Handwritten)