Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

A quarter is worth $0.25\$0.25 and a half dollar is worth $0.50\$0.50.\newlinea. A quarter has a diameter of 1516\frac{15}{16} inch and a height of 116\frac{1}{16} inch. Find the surface area of a quarter. Round your answer to the nearest hundredth.\newlineb. A half dollar has a diameter of 98\frac{9}{8} inches and a height of 332\frac{3}{32} inch. Find the surface area of a half dollar. Round your answer to the nearest hundredth.

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Grade 6right chevron icon
Area of quadrilaterals and triangles: word problemsright chevron icon

Full solution

Q. A quarter is worth $0.25\$0.25 and a half dollar is worth $0.50\$0.50.\newlinea. A quarter has a diameter of 1516\frac{15}{16} inch and a height of 116\frac{1}{16} inch. Find the surface area of a quarter. Round your answer to the nearest hundredth.\newlineb. A half dollar has a diameter of 98\frac{9}{8} inches and a height of 332\frac{3}{32} inch. Find the surface area of a half dollar. Round your answer to the nearest hundredth.
  1. Calculate Radius of Quarter: To find the surface area of a quarter, we need to calculate the area of the two circular faces and the area of the side (which is a rectangle when unrolled). The formula for the area of a circle is A=πr2A = \pi r^2, where rr is the radius. The formula for the area of a rectangle is A=lwA = lw, where ll is the length and ww is the width. The length of the rectangle will be the circumference of the circle, which is C=πdC = \pi d, where dd is the diameter. The width of the rectangle is the height of the quarter.\newlineFirst, we calculate the radius of the quarter by dividing the diameter by 22.\newlineRadius of a quarter = (15/16 inch)/2=(15/32 inch)(15/16 \text{ inch}) / 2 = (15/32 \text{ inch})
  2. Calculate Area of Quarter Face: Now we calculate the area of one circular face of the quarter using the radius.\newlineArea of one face = π×(1532 inch)2\pi \times (\frac{15}{32} \text{ inch})^2\newline= π×(2251024 inch2)\pi \times (\frac{225}{1024} \text{ inch}^2)\newline= π×(0.2197265625 inch2)\pi \times (0.2197265625 \text{ inch}^2)
  3. Calculate Total Area of Quarter: Since there are two faces, we multiply the area of one face by 22.\newlineTotal area of both faces = 2×π×(0.2197265625 inch2)2 \times \pi \times (0.2197265625 \text{ inch}^2)\newline= 2×π×0.2197265625 inch22 \times \pi \times 0.2197265625 \text{ inch}^2\newline= π×0.439453125 inch2\pi \times 0.439453125 \text{ inch}^2
  4. Calculate Circumference of Quarter: Next, we calculate the circumference of the quarter to find the length of the rectangle (side area).\newlineCircumference = π×\pi \times diameter\newline= π×(1516 inch)\pi \times (\frac{15}{16} \text{ inch})\newline= π×0.9375 inch\pi \times 0.9375 \text{ inch}
  5. Calculate Area of Quarter Rectangle: The width of the rectangle is the height of the quarter.\newlineWidth of the rectangle (height of the quarter) = (116 inch)(\frac{1}{16} \text{ inch})
  6. Calculate Total Surface Area of Quarter: Now we calculate the area of the rectangle (side area).\newlineArea of the rectangle = Circumference * Height\newline= π×0.9375 inch×(116 inch)\pi \times 0.9375 \, \text{inch} \times \left(\frac{1}{16} \, \text{inch}\right)\newline= (π×0.9375 inch)/16\left(\pi \times 0.9375 \, \text{inch}\right) / 16\newline= π×0.05859375 inch2\pi \times 0.05859375 \, \text{inch}^2
  7. Calculate Surface Area of Quarter: We add the total area of both faces to the area of the rectangle to find the total surface area of the quarter.\newlineTotal surface area of the quarter = π×0.439453125 inch2+π×0.05859375 inch2\pi \times 0.439453125 \text{ inch}^2 + \pi \times 0.05859375 \text{ inch}^2\newline= π×(0.439453125 inch2+0.05859375 inch2)\pi \times (0.439453125 \text{ inch}^2 + 0.05859375 \text{ inch}^2)\newline= π×0.498046875 inch2\pi \times 0.498046875 \text{ inch}^2
  8. Calculate Radius of Half Dollar: Now we use the value of π\pi (approximately 3.141593.14159) to calculate the numerical value of the total surface area and round it to the nearest hundredth.\newlineTotal surface area of the quarter ≈3.14159×0.498046875 inch2\approx 3.14159 \times 0.498046875 \text{ inch}^2\newline≈1.5648 inch2\approx 1.5648 \text{ inch}^2\newlineRounded to the nearest hundredth, the surface area of the quarter is approximately 1.56 inch21.56 \text{ inch}^2.
  9. Calculate Area of Half Dollar Face: Next, we move on to part b of the problem, which is to find the surface area of a half dollar. We will use the same method as we did for the quarter.\newlineFirst, we calculate the radius of the half dollar by dividing the diameter by 22.\newlineRadius of a half dollar = (9/8 inches)/2=(9/16 inches)(9/8\,\text{inches}) / 2 = (9/16\,\text{inches})
  10. Calculate Total Area of Half Dollar: Now we calculate the area of one circular face of the half dollar using the radius.\newlineArea of one face = π×(916 inches)2\pi \times (\frac{9}{16} \text{ inches})^2\newline= π×(81256 inches2)\pi \times (\frac{81}{256} \text{ inches}^2)\newline= π×(0.31640625 inches2)\pi \times (0.31640625 \text{ inches}^2)
  11. Calculate Circumference of Half Dollar: Since there are two faces, we multiply the area of one face by 22.\newlineTotal area of both faces = 2×π×(0.31640625 inches2)2 \times \pi \times (0.31640625 \text{ inches}^2)\newline= 2×π×0.31640625 inches22 \times \pi \times 0.31640625 \text{ inches}^2\newline= π×0.6328125 inches2\pi \times 0.6328125 \text{ inches}^2
  12. Calculate Area of Half Dollar Rectangle: Next, we calculate the circumference of the half dollar to find the length of the rectangle (side area).\newlineCircumference = π×diameter\pi \times \text{diameter}\newline= π×(98 inches)\pi \times \left(\frac{9}{8} \text{ inches}\right)\newline= π×1.125 inches\pi \times 1.125 \text{ inches}
  13. Calculate Total Surface Area of Half Dollar: The width of the rectangle is the height of the half dollar.\newlineWidth of the rectangle (height of the half dollar) = (332(\frac{3}{32} inches)
  14. Calculate Surface Area of Half Dollar: Now we calculate the area of the rectangle (side area).\newlineArea of the rectangle = Circumference×Height\text{Circumference} \times \text{Height}\newline= π×1.125 inches×(332 inches)\pi \times 1.125 \text{ inches} \times \left(\frac{3}{32} \text{ inches}\right)\newline= (π×1.125 inches)×(332 inches)\left(\pi \times 1.125 \text{ inches}\right) \times \left(\frac{3}{32} \text{ inches}\right)\newline= π×0.10546875 inches2\pi \times 0.10546875 \text{ inches}^2
  15. Calculate Surface Area of Half Dollar: Now we calculate the area of the rectangle (side area).\newlineArea of the rectangle = Circumference×Height\text{Circumference} \times \text{Height}\newline= π×1.125 inches×(332 inches)\pi \times 1.125 \text{ inches} \times \left(\frac{3}{32} \text{ inches}\right)\newline= (π×1.125 inches)×(332 inches)(\pi \times 1.125 \text{ inches}) \times \left(\frac{3}{32} \text{ inches}\right)\newline= π×0.10546875 inches2\pi \times 0.10546875 \text{ inches}^2 We add the total area of both faces to the area of the rectangle to find the total surface area of the half dollar.\newlineTotal surface area of the half dollar = π×0.6328125 inches2+π×0.10546875 inches2\pi \times 0.6328125 \text{ inches}^2 + \pi \times 0.10546875 \text{ inches}^2\newline= π×(0.6328125 inches2+0.10546875 inches2)\pi \times (0.6328125 \text{ inches}^2 + 0.10546875 \text{ inches}^2)\newline= $\pi \times \(0\).\(73828125\) \text{ inches}^\(2\)
  16. Calculate Surface Area of Half Dollar: Now we calculate the area of the rectangle (side area).\(\newline\)Area of the rectangle = Circumference \(\times\) Height\(\newline\)\(= \pi \times 1.125 \, \text{inches} \times (\frac{3}{32} \, \text{inches})\)\(\newline\)\(= (\pi \times 1.125 \, \text{inches}) \times (\frac{3}{32} \, \text{inches})\)\(\newline\)\(= \pi \times 0.10546875 \, \text{inches}^2\) We add the total area of both faces to the area of the rectangle to find the total surface area of the half dollar.\(\newline\)Total surface area of the half dollar \(= \pi \times 0.6328125 \, \text{inches}^2 + \pi \times 0.10546875 \, \text{inches}^2\)\(\newline\)\(= \pi \times (0.6328125 \, \text{inches}^2 + 0.10546875 \, \text{inches}^2)\)\(\newline\)\(= \pi \times 0.73828125 \, \text{inches}^2\) Now we use the value of \(\pi\) (approximately \(3\).\(14159\)) to calculate the numerical value of the total surface area and round it to the nearest hundredth.\(\newline\)Total surface area of the half dollar \(\approx 3.14159 \times 0.73828125 \, \text{inches}^2\)\(\newline\)\(\approx 2.3193 \, \text{inches}^2\)\(\newline\)Rounded to the nearest hundredth, the surface area of the half dollar is approximately \(= \pi \times 1.125 \, \text{inches} \times (\frac{3}{32} \, \text{inches})\)\(0\).

More problems from Area of quadrilaterals and triangles: word problems

Question
Skyler climbs a watchtower to guard against forest fires.\newlineThe function R(h)=13hR(h)=\sqrt{13h} gives the distance, in kilometers, that Skyler can see when their eyes are hh meters above the ground.\newlineThe function A(d)=πd2A(d)=\pi d^{2} gives the area, in square kilometers, that Skyler can guard when they can see a distance of dd kilometers.\newlineWhich expression models the area Skyler can guard when their eyes are hh meters above the ground?\newlineChoose 11 answer:\newline(A) 13πh13\pi h\newline(B) 13πh213\pi h^{2}\newline(C) 13πh2\sqrt{13\pi h^{2}}\newline(D) 169πh2169\pi h^{2}
Get tutor helpright-arrow

Posted 8 months ago

Question
After the outbreak of a mysterious disease, the average wait time at a hospital increased by 70%70\%. Before the outbreak, the average wait time at the hospital was mm minutes.\newline Which of the following expressions could represent the average wait time at the hospital after the outbreak?\newline Choose 22 answers:\newline A 0.7m0.7m\newline B 170100m\frac{170}{100}m\newline C m+70m+70\newline D m+0.7m+0.7\newline E 1.7m1.7m
Get tutor helpright-arrow

Posted 7 months ago

Question
The radius of a semicircle is 33 yards. What is the semicircle's area?\newlineUse π≈3.14\pi \approx 3.14 and round your answer to the nearest hundredth.\newlinesquare yards
Get tutor helpright-arrow

Posted 8 months ago

Question
\newlineA man has bent a circular wire of radius 49cm49\text{cm} to form a square. Find the sides of a square.\newlineA)100cmA)100\text{cm}\newlineB)50cmB)50\text{cm}\newlineC)98cmC)98\text{cm}
Get tutor helpright-arrow

Posted 8 months ago

Question
The hypotenuse of a right triangle measures 17 cm 17 \mathrm{~cm} and one of its legs measures 8 cm 8 \mathrm{~cm} . Find the measure of the other leg. If necessary, round to the nearest tenth.\newlineAnswer: □\square cm \mathrm{cm}
Get tutor helpright-arrow

Posted 8 months ago

Question
One of the legs of a right triangle measures 15 cm 15 \mathrm{~cm} and its hypotenuse measures 17 cm 17 \mathrm{~cm} . Find the measure of the other leg. If necessary, round to the nearest tenth.\newlineAnswer: □\square cm \mathrm{cm}
Get tutor helpright-arrow

Posted 9 months ago

Question
One of the legs of a right triangle measures 8 cm 8 \mathrm{~cm} and the other leg measures 15 cm 15 \mathrm{~cm} . Find the measure of the hypotenuse. If necessary, round to the nearest tenth.\newlineAnswer: □\square cm \mathrm{cm}
Get tutor helpright-arrow

Posted 8 months ago

Question
Find the volume of a right circular cone that has a height of 7.4 cm 7.4 \mathrm{~cm} and a base with a radius of 8.1 cm 8.1 \mathrm{~cm} . Round your answer to the nearest tenth of a cubic centimeter.\newlineAnswer: cm3 \mathrm{cm}^{3}
Get tutor helpright-arrow

Posted 9 months ago

Question
Find the volume of a right circular cone that has a height of 13.3ft 13.3 \mathrm{ft} and a base with a diameter of 9.4ft 9.4 \mathrm{ft} . Round your answer to the nearest tenth of a cubic foot.\newlineAnswer: ft3 \mathrm{ft}^{3}
Get tutor helpright-arrow

Posted 9 months ago

Question
You pick a card at random, put it back, and then pick another card at random.\newline44\newline55\newline66\newline77\newlineWhat is the probability of picking a number greater than 55 and then picking a 44 ?\newlineWrite your answer as a percentage.
Get tutor helpright-arrow

Posted 1 month ago

View all (59)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant