University:
Glendale Community College
Course:
MAT142 | College Mathematics
Academic year:

2020
Views:

448

Pages:

12
Author:

brnknoutel

Section 2.2 Solutions Homework #1-4: Find the circumference of each circle. Make sure to include the proper units in your answer. Leave your answer in terms of 𝜋. 1) 𝐶 = 2𝜋𝑟 C = 2𝜋(14𝑚) Answer: 28𝜋 m 3) C = 𝜋𝑑 Answer: 16𝜋 𝑐𝑚 5) P = 2(8cm + 4cm) P = 2(12 cm) Answer: 24 cm 7) Assume opposite sides have equal lengths. Don’t include the 3 cm when finding the perimeter. It is the height, and not one of the sides. P = 4 cm + 4 cm + 10 cm + 10 cm P = 28 cm 9) P = 124 ft + 156 ft + 156 ft Answer: 436 ft 11) P = 5 in + 8 in + 3 in + 4 in Answer: 20 in Homework: #13 – 24 Find the area of each figure. Use appropriate units. 13) Assume the lengths are in inches. Area = (25𝑖𝑛)(18𝑖𝑛) 2 Area = 225 in2 15) Area = (10𝑚)(14𝑚) 2 Answer: 70m2 17) Find “a”, then find the area of the triangle. Assume lengths are given in inches. a2 + 242 = 252 a2 + 576 = 625 a2 = 49 a = 7 in Area = (24𝑖𝑛)(7𝑖𝑛) 2 Area = 84 in2 19) Find “t”, then find the area of the triangle. Assume lengths are given in centimeters. t2 + 122 = 132 t2 + 144 = 169 t2 = 25 t=5 Area = (12𝑐𝑚)(5𝑐𝑚) 2 Answer: 30 cm2 21) Area = (3cm)(10cm) Answer: 30 cm2 23) A = (10.3 cm)(6.2 cm) Answer: 63.86 cm2 25). Area = (13.4 𝑚+7.2𝑚)(10.6𝑚) 2 Area= 128.26 m2 27) Area = (20 𝑐𝑚+6𝑐𝑚)(10𝑐𝑛) 2 Area = (260 cm2)/2 Answer: 130 cm2 29) Area = (3𝑚+6𝑚)(4𝑚) 2 Area = (36m2)/2 Answer: 18 m2 31) A = (9cm)(16cm) Answer: 144 cm2 33) Assume units are given in inches. A = (8 in)2 Answer: 64 in2 35) A = 𝜋(4𝑐𝑚)2 Answer: 16𝜋 𝑐𝑚2 37) Diameter = 6” radius = 3” A = 𝜋(3")2 Answer: 9𝜋 𝑠𝑞𝑢𝑎𝑟𝑒 𝑖𝑛𝑐ℎ𝑒𝑠 39) Radius = 8 cm A = 𝜋(8𝑐𝑚)2 Answer: 64𝜋 cm2 Homework #41-56: Find the area of the shaded region. Use appropriate units. 41) use 3.14 for 𝜋 First calculate the area as if the entire shape was shaded. Area if entire shape was shaded: Area all shaded = (18cm)(12cm) = 216 cm2 Next find the area of the unshaded region. Area unshaded = 3.14(4cm)2 = 50.24 cm2 Finally subtract the results. Answer: 216 cm2 – 50.24 cm2 = 165.76 cm2 43) Leave your answer in terms of 𝜋. Assume measurements are given in feet. First calculate the area as if the entire shape was shaded. Area all shaded = 𝜋(10𝑓𝑡)2 = 100𝜋 𝑓𝑡 2 Next find the area of the unshaded region. Area unshaded = 𝜋(5𝑓𝑡)2 = 25𝜋 𝑓𝑡 2 Finally subtract the amounts. Answer: 100𝜋 𝑓𝑡 2 − 25𝜋 𝑓𝑡 2 = 75𝜋 𝑓𝑡 2 45) Use 3.14 for 𝜋. Assume measurements are given in meters. First calculate the area as if the entire shape was shaded. Area if entire shape was shaded: This is a circle with radius 5 m. Area all shaded = 3.14(5m)2 = 78.5 m2 Next find the area of the unshaded region. Area unshaded = (7m)2 = 49 m2 Finally subtract the amounts. Answer: 78.5 m2 – 49 m2 = 29.5 m2 47) Find the length of the diagonal “d” rounded to 2 decimals. Use “d” to find the radius. Round the radius to 2 decimals. Then find the shaded area. Use 3.14 for 𝜋. Assume measurements are given in meters I need to use the Pythagorean theorem to find the length of the diagonal. 22 + 22 = c2 8 = c2 Diagonal = 2.83 m Divide by two to get the radius Radius = 1.42 m First calculate the area as if the entire shape was shaded. Area all shaded = 3.14(1.42 m)2 = 6.33 m2 Next find the area of the unshaded region. Area unshaded = (2m)2 = 4m2 Now subtract Shaded area = 6.33m2 – 4 m2 Answer: 2.33 m 2 49) First calculate the area as if the entire shape was shaded. Area all shaded = (15mm)2 = 225mm2 Next find the area of the unshaded region. Area unshaded = (5mm)2 = 25mm2 Finally subtract the results Answer: 225 mm2 – 25 mm2 = 200 mm2 51) First calculate the area as if the entire shape was shaded. Area all shaded = (30cm)(15cm)= 450 cm2 Next find the area of the unshaded region. Area unshaded = (11cm)(22cm) = 242 cm2 Finally subtract the amounts Answer: 450 cm2 – 242 cm2 = 208 cm2 53) Use 3.14 for 𝜋. Assume lengths are given First calculate the area as if the entire shape in centimeters. Round your answer to 2 was shaded. decimals. The entire shape is a square that measures 12 cm on each side. Area all shaded = (12cm)2 = 144cm2 Next find the area of the unshaded region. If we put the unshaded region together we get a circle of radius of 6 cm. Area unshaded = 3.14(6cm)2 = 113.04 cm2 Finally subtract the amounts. Answer: 144 cm2 – 113.04 cm2 = 30.96 cm2