kiran bent some wire around a rectangle to make a picture frame. the rectangle is 8 inches by 10 inches. find the length of the wire used to make the picture frame.

what is the diameter of each circle? 2 in

how many semicircles are there? 16

how many $\frac{3}{4}$ circles are there? 4

how many complete circles are used to make the wire frame? 11 circles

what is the approximate length of the wire used to make the picture frame? use 3.14 for $\pi$. 62.8 in

Question

kiran bent some wire around a rectangle to make a picture frame. the rectangle is 8 inches by 10 inches. find the length of the wire used to make the picture frame.

what is the diameter of each circle? 2 in

how many semicircles are there? 16

how many $\frac{3}{4}$ circles are there? 4

how many complete circles are used to make the wire frame? 11 circles

what is the approximate length of the wire used to make the picture frame? use 3.14 for $\pi$. 62.8 in

Accepted Answer

{ "quality": "clear", "question_count": 5, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Diameter Measurement", "Circumference Formula" ], "new_concepts": [], "current_concepts": [ "Diameter Measurement", "Circumference Formula", "Composite Perimeter" ] } ## Determine the diameter of each circle and count the arcs $$ \begin{aligned} &\text{Rectangle dimensions: } 8\text{ in by } 10\text{ in}\ &\text{Number of semicircles along the short side (8 in): } 4 \implies d = \frac{8}{4} = 2\text{ in}\ &\text{Number of semicircles along the long side (10 in): } 5 \implies d = \frac{10}{5} = 2\text{ in}\ &\text{Total semicircles along the 4 straight edges: } 2 \times (4 + 5) = 18\ &\text{Number of } \frac{3}{4}\text{ circles at the 4 corners: } 4 \end{aligned} $$ ## Calculate the total number of complete circles $$ \begin{aligned} &\text{Equivalent circles from semicircles: } \frac{18}{2} = 9\ &\text{Equivalent circles from corner arcs: } 4 \times \frac{3}{4} = 3\ &\text{Total complete circles: } 9 + 3 = 12 \end{aligned} $$ ## Calculate the approximate length of the wire $$ \begin{aligned} &C = \pi \times d = 3.14 \times 2 = 6.28\text{ in}\ &\text{Total length} = 12 \times C = 12 \times 6.28 = 75.36\text{ in} \end{aligned} $$ ## Question 1 What is the diameter of each circle? 2 in ## Question 2 How many semicircles are there? 18 ## Question 3 How many $\frac{3}{4}$ circles are there? 4 ## Question 4 How many complete circles are used to make the wire frame? 12 circles ## Question 5 What is the approximate length of the wire used to make the picture frame? Use 3.14 for $\pi$. 75.36 in { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Geometry", "Circumference Formula" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Determine the diameter of each circle and count the arcs

Calculate the total number of complete circles

Calculate the approximate length of the wire

Answer:

Question 1

Question 2

Question 3

Question 4

Question 5