Question

THE SLANT HEIGHT OF THE FRUSTUM OF A CONE IS 4CM AND THE PERIMETER OF CIRCULAR ENDS ARE 18 CM AND 6CM. THE CURVED SURFACE AREA OF THE FRUSTUM IS

Answer 1

✪ $\huge{\red{\underline{\overline{\mathbf{Question}}}}}$ ✪

→THE SLANT HEIGHT OF THE FRUSTUM OF A CONE IS 4CM AND THE PERIMETER OF CIRCULAR ENDS ARE 18 CM AND 6CM. THE CURVED SURFACE AREA OF THE FRUSTUM IS

✪ $\huge{\green{\underline{\overline{\mathbf{Answer}}}}}$ ✪

⇒Given:

• L = 4 cm
• Perimeter of Upper end = 18 cm
• Perimeter of Lower end = 6 cm

⇒To Find:

• C.S.A. of Frustum

⇒Radius of Upper End -

⇒$2\times \pi \times R_1=18$

⇒$R_1=\frac{18}{3.14\times 2}$

⇒$R_1=2.8\:cm$ [approx.]

⇒Radius of Lower End -

⇒$2\times \pi \times R_2=6$

⇒$R_2=\frac{6}{3.14\times 2}$

⇒$R_2=0.95$ [approx.]

Using formula of C.S.A.

⇒$\pi \times (R_1+R_2)\times l$

⇒$3.14\times(2.8+0.95)\times 10$

⇒$31.4\times 3.75$

⇒$\huge{\pink{\overbrace{\underbrace{117.75 \:cm^{\small{2}}}}}}$

________________________________________

Formulas Used :-

• $Perimeter=2\times \pi \times r$
• $C.S.A. \:of \:Frustum-$
• $\pi \times (R_1+R_2)\times l$

★━★━★━★━★━★━★━★━★━★━★

▂ ▄ ▅ ▆ ▇ █⚡ ᗩᖇƳᗩᑎ ⚡█ ▇ ▆ ▅ ▄ ▂

★━★━★━★━★━★━★━★━★━★━★

Answer 2

Given,

Slant height of frustum of cone (l) = 4 cm

Let ratio of the top and bottom circles be r1 and r2

And given perimeters of its circular ends as 18 cm and 6 cm

⟹ 2πr1 = 18 cm; 2πr2 = 6 cm

⟹ πr1= 9 cm and πr2 = 3 cm

We know that,

Curved surface area of frustum of a cone = π(r1 + r2)l

= (πr1+πr2)l = (9 + 3) × 4

 = (12) × 4 = 48 cm2

Therefore, the curved surface area of the frustum = 48 cm2.