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inysia [295]
2 years ago
9

What is the ratio of the surface areas of two cones if the radius of one is 3 en and the slant height is 7 cm, and the other has

a radius of 5 cm and a slan Height of 9 cm?​
Mathematics
1 answer:
Vsevolod [243]2 years ago
3 0

<u>Given</u><u> </u><u>Information</u><u> </u><u>:</u><u>-</u>

⠀

A cone with dimensions :-

  • Radius = 3 cm
  • Slant height ( l ) = 7 cm

⠀

Another cone with dimensions :-

⠀

  • Radius = 5 cm
  • Slant height = 9 cm

⠀

<u>To</u><u> </u><u>Find</u><u> </u><u>:</u><u>-</u>

⠀

  • The ratio of their total surface area

⠀

<u>Formula</u><u> </u><u>Used</u><u> </u><u>:</u><u>-</u>

⠀

\qquad \diamond \:  \underline{ \boxed{ \red{ \sf T.S.A._{Cone}= \pi r(r+l) }}} \:  \star

⠀

<u>Solution</u><u> </u><u>:</u><u>-</u>

⠀

For the first cone,

⠀

Since, we don't really have to find the exact values of the surface area, we will let pi remain as a sign itself, this will make the calculations easier.

⠀

\sf \longrightarrow T.S.A. = \pi  \times 3(3 + 7) \\  \\  \\  \sf \longrightarrow T.S.A. = \pi \times 3 \times 10 \:  \:  \:   \\  \\  \\  \sf \longrightarrow T.S.A. =30 \pi  \: {cm}^{2}  \:  \:  \:  \:  \:  \:  \:  \:  \\  \\

Now, for the second cone,

⠀

\sf \longrightarrow T.S.A. = \pi \times 5(5 + 9) \\  \\  \\ \sf \longrightarrow T.S.A. = \pi  \times 5 \times 14 \:  \:  \:   \:  \\  \\  \\   \sf \longrightarrow T.S.A. =70 \pi \:  {cm}^{2}  \:  \:  \:  \:  \:  \:  \:  \:  \:  \\  \\

Now, we just have to calculate the ratio of their surface areas, thus,

⠀

\sf \longrightarrow Ratio =  \dfrac{Surface ~area~of~first~cone}{Surface ~area~of~second~cone}  \\  \\  \\ \sf \longrightarrow Ratio =  \frac{30 \pi \:  {cm}^{2} }{70 \pi \:  {cm}^{2}  } \:  \:  \:  \:  \:  \:  \:  \:  \:  \qquad \qquad \qquad \\  \\  \\  \sf \longrightarrow Ratio =  \frac{ 3 \cancel{0 \pi \:  {cm}^{2}} }{ 7 \cancel{0 \pi \:   {cm}^{2} } } \qquad \qquad \qquad \qquad \\  \\  \\\sf \longrightarrow Ratio =  \frac{3}{7}   = 3 : 7 \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \\  \\

Thus, the ratio between the surface areas of the cones is 3 : 7.

⠀

\underline{ \rule{227pt}{2pt}} \\  \\

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