University:
Augusta University
Course:
MATH 4800 | Secondary Mathematics from an Advanced Perspective
Academic year:

2024
Views:

185

Pages:

2
Author:

Autumn Cox

Question 1 Which shape of the net of a cylinder represents the lateral surface area of the cylinder? Answer The lateral surface area is the blue part. If we were to remove the yellow bases and cut the blue surface vertically then unroll it, you will obtain a rectangle. Question 2 Soda is sold in aluminum cans that measure 4.83 inches in height and 2.6 inches in diameter. Use 3.14 for π. What is the volume? Answer The volume of a cylinder, the shape of the can, is given by: V = πr²h Substitute π = 3.14, r = 2.6/2 = 1.3 inches and h = 4.83 inches: V = (3.14)(1.3)²(4.83) V ≈ 25.63 in³ Question 3 The height of the cone 19 ft and the radius is 9 ft, what is the volume? Answer The volume of a cone with radius r and height h is given by: V = (1/3)πr²h Substitute r=9 ft and h=19 ft: V = (1/3)π(9)²(19) V ≈ 513π ≈ 1611.63 ft³ Question 4 Find the area of the regular polygon with the specified side length s and apothem a. decagon, with a = 10 m and s = 6.5 m Answer Use A = (1/2)ans Substitute n=10, a=10 m, and s=6.5 m: A = (1/2)(10)(10)(6.5) A = 325 The result: 325m². Question 5 The perimeter of a rectangle is 56 in. The ratio of the length to the width is 6:1. Find the length and the width. Answer Using the given ratio, we let 6x be the length and x be the width. The perimeter of a rectangle is given by: P = 2l + 2w Substituting given, we have: 56 = 2(6x) + 2(x) Solve for x: 56 = 12x + 2x 56 = 14x 56/14 = x 4 = x So, the length is 6(4) = 24 inches and the width is 4 inches.