Question

Radius ( r ), Diameter ( d ), Circumference ( c )

i. r = 7 cm, d = ?, c = ?
ii. r = ?, d = 28 cm, c = ?
iii. r = ? d = ? c = 616 cm

Answer 1

Answer:

Radius ( r ), Diameter ( d ), Circumference ( c )

• Formula used : c = 2πr, d = 2r

i. r = 7 cm, d = 14 cm, c = 44 cm

ii. r = 14 cm, d = 28 cm, c = 88 cm

iii. r = 98 cm, d = 196 cm, c = 616 cm

Answer 2

Given: Rαdius (r) = 7 cm

To find: Diαmeter (d), & Circumference (c)

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To find the diαmeter,

❍ As we know thαt:

$\star \; \underline{\boxed{\sf{\purple{d_{\pink{(diameter)}} = 2r _{(\pink{2 \times radius})}}}}}$

   

$:\implies \; \sf{d = 2r}\\\\:\implies \; \sf{d = 2 \times radius}\\\\:\implies \; \sf{d = 2 \times 7}\\\\:\implies \; \underline{\boxed{\sf{\pink{d = 14cm}}}} \; \bigstar$

     

To find the circumference,

❍ As we know thαt:

$\star \; \underline{\boxed{\sf{\purple{c_{\pink{(circumference)}} = \pi d _{(\pink{\pi \times diameter})}}}}}$

     

$:\implies \; \sf{c = \pi d}\\\\:\implies \; \sf{c = \pi \times diameter}\\\\:\implies \; \sf{c = \dfrac{22}{7} \times diameter}\\\\:\implies \; \sf{c = \dfrac{22}{\cancel{7}} \times \cancel{14} }\\\\:\implies \; \sf{c = 22 \times 2}\\\\:\implies \; \underline{\boxed{\sf{\pink{c = 44cm}}}} \; \bigstar$

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Given: Diαmeter (d) = 28 cm

To find: Rαdius (r), & Circumference (c)

⠀⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

     

To find the rαdius,

❍ As we know thαt:

$\star \; \underline{\boxed{\sf{\purple{r_{\pink{(radius)}} = \dfrac{1}{2} \times d _{(\pink{\frac{1}{2} \times diameter})}}}}}$

$:\implies \; \sf{r = \dfrac{1}{2} \times d}\\\\:\implies \; \sf{d = \dfrac{1}{\cancel{2}} \times \cancel{28}}\\\\:\implies \; \underline{\boxed{\sf{\pink{r = 14 cm}}}} \; \bigstar$

   

To find the circumference,

❍ As we know thαt:

$\star \; \underline{\boxed{\sf{\purple{c_{\pink{(circumference)}} = \pi d _{(\pink{\pi \times diameter})}}}}}$

     

$:\implies \; \sf{c = \pi d}\\\\:\implies \; \sf{c = \pi \times diameter}\\\\:\implies \; \sf{c = \dfrac{22}{7} \times diameter}\\\\:\implies \; \sf{c = \dfrac{22}{\cancel{7}} \times \cancel{28} }\\\\:\implies \; \sf{c = 22 \times 4}\\\\:\implies \; \underline{\boxed{\sf{\pink{c = 88cm}}}} \; \bigstar$

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Given:  Circumference (c) = 616

To find: Rαdius (r), & Diαmeter (d)

⠀⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

     

To find the diameter,

❍ As we know thαt:

$\star \; \underline{\boxed{\sf{\purple{c_{\pink{(circumference)}} = \pi d _{(\pink{\pi \times diameter})}}}}}$

     

$:\implies \; \sf{c = \pi d}\\\\:\implies \; \sf{616 = \dfrac{22}{7} \times 7}\\\\:\implies \; \sf{\dfrac{\cancel{616} \times 7}{\cancel{22}}}\\\\:\implies \; \sf{28 \times 7}\\\\:\implies \; \underline{\boxed{\sf{\pink{d = 196cm}}}} \; \bigstar$

         

To find the rαdius,

❍ As we know thαt:

$\star \; \underline{\boxed{\sf{\purple{r_{\pink{(radius)}} = \dfrac{1}{2} \times d _{(\pink{\frac{1}{2} \times diameter})}}}}}$

     

$:\implies \; \sf{r = \dfrac{1}{2} \times d}\\\\:\implies \; \sf{d = \dfrac{1}{\cancel{2}} \times \cancel{196}}\\\\:\implies \; \underline{\boxed{\sf{\pink{r = 98 cm}}}} \; \bigstar$

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Answer:

• r = 7 cm, d = 14 cm, c = 44 cm
• r = 14 cm, d = 28 cm, c = 88 cm
• r = 98 cm, d = 196,c = 616 cm