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

2024
Views:

295

Pages:

2
Author:

Autumn Cox

Question 1 Find the volume of the prism. length=60cm, breadth=20cm, height =10cm Answer Volume of the prism = l * w * h = 60 * 20 * 10 = 12000 Question 2 The length of a rectangle is 4 cm less than twice its width. Its perimeter is 40 cm. Find its length and width. Answer Let x be the width so that 2x-4 is the length, both in cm. The perimeter of a rectangle is given by: P=2l+2w where l is the length and w is the width. Given a perimeter of 40 cm, we can write: 40=2(2x-4)+2(x) Solve for x. Divide both sides by 2: 20=(2x-4)+x 20=3x-4 24=3x 8=x So, the dimensions of the rectangle are: length: 2x-4=2(8)-4=12cm width: x=8 cm Question 3 A banner is made of a square and a semicircle. The square has side lengths of 26 inches. One side of the square is also the diameter of the semicircle. What is the total area of the banner? Use 3.14 for π. Answer The total area of the banner is the sum of the areas of the square and the semicircle (half circle) The side length of the square is 26 inches and the radius of the semicircle is 13 inches (half of the diameter) so: A = A_square + A_semicircle A = (s²) + (1/2πr²) A = (26²) + (1/2)(3.14)(13)² A = 676 + 265.33 A ≈ 941.33 square inches. Question 4 A wire of length r feet is bent into a rectangle whose width is 2 times its height. Write the area A of the rectangle as a function of the wires Answer The length of the wire is the perimeter of the rectangle with width w and height h: 2w + 2h = r Given that the width is 2 times its height, w = 2h, we write: 2(2h) + 2h = r 4h + 2h = r 6h = r h = r/6 which follows that: w = 2h = 2(r/6) = r/3 The area of the rectangle is: A = wh In terms of r, A = (r/3)(r/6) A = r²/18 Solve for r in terms of A: 18A = r² √18A = r or r = 3√2A 26.6s