Question

hello.. answer is only if u know.. otherwise I will report...with full explanation ​

Answer 1

Answer:

$\huge\underline\bold\red{Answer!!}$

Slant height of the frustum

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: l = \sqrt{(R - r) {}^{2} } + h1 {}^{2}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \sqrt{(9 - 4) {}^{2} + 12 {}^{2} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \sqrt{5 {}^{2} + 12 {}^{2} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \sqrt{25 + 144}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \sqrt{169}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 13cm$

$outer \: surface \: area = 2\pi \: rh2 + \pi(R + r)l \: sq.units$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \pi(2rh2 + (R + r)l)$

$\: \: \: \: \: \: \: \: = \pi(2 \times 4 \times 10 + (9 + 4)13)$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \pi(80 + 169)$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \pi \times 249$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 781.86cm {}^{2}$

:. Area of the sheet required to make the funnel = 782cm²

Hope it helps you ❤️ ✨

Answer 2

Your Question:

An oil funnel made of tin sheet consists of a 10 cm long cylindrical portion attached to a frustum of a cone. If the total height is 22 cm, diameter of the cylindrical portion is 8 cm and the diameter of the top of the funnel is 18 cm, find the area of the tin sheet required to make the funnel.

Your Answer:

We have,

Upper Radius(R) of Frustum ABEF = 18/2 = 9cm

Lower Radius(r) of Frustum ABEF = 8/2 = 4cm

Height of Frustum$(h_1)$ = 22 - 10 =12cm

Slant Height of Frustum=

$\tt \sqrt{(R-r)^2 + {h_1}^2} \\\\ \tt \Rightarrow \sqrt{(9-4)^2+12^2} \\\\ \tt \Rightarrow \sqrt{25+144} \\\\ \tt \Rightarrow \sqrt{169} \\\\ \tt = 13$

Height of Cylinder $(h_2)$ = 10cm

Radius of Cylinder(r) = 4cm

Area of tin sheet required = CSA of frustum part + CSA of cylindrical part =

$\tt \pi (R+r)l + 2\pi rh_2 \\\\ \tt = \dfrac{22}{7} \times (9+4) \times 13 + 2 \times \dfrac{22}{7} \times 4 \times 10 \\\\ \tt = \dfrac{22}{7}(13\times 13 + 2\times 4 \times 10) \\\\ \tt = \dfrac{22}{7}(169+80) \\\\ \tt = \dfrac{22}{7} \times 249 \\\\ \tt = 782.6cm^2$