Question

the curved surface area of the frustum of a cone is 180 square cm and the circumference of its circular bases are 18 cm and 6 cm respectively find the slant height of the frustum of a cone​

Answer 1

꧁SOLUTION ꧂

✧♥༻༺♥✧

✼GIVEN✼

• CSA of frustum=180cm²
• Circumference of its bases are 18cm , 6cm
• C¹=18cm
• C²=6cm

✼LET

• Radius 1 be r¹
• Radius 2 be r²

✼By using formula of circumference of circle✼

• 2πr¹=18
• πr¹=9
• r¹=9/π

✼Similarly , using same formula✼

• 2πr²=6
• πr²=3
• r²=3/π

✼Find the slant height of the frustum of cone✼

• Using formula of CSA

$⇒csa \: of frustum \: cone = \pi \: l( {r}^{1} + {r}^{2} ) \\ \\ ⇒\pi \: ( \frac{9}{\pi} + \frac{3}{\pi})l = 180 \\ \\ ⇒\pi( \frac{9 + 3}{\pi} )l = 180 \\ \\ ⇒\pi \times \frac{12}{\pi} \times l = 180 \\ \\ ⇒12l = 180 \\ \\ ⇒l = 15cm$

✼Hence:-

• Slant height of frustum cone is 15cm