Question

a hip of rice is in the form of a cone of base diameter 24m and height 3.5m.find the volume of rice.how much canvas cloth is required to just cover the hip

Answer 1

Answer :

Given, Diameter of hip = 24 m

Therefore radius (r) = diameter ÷ 2 = 24 ÷ 2 = 12m

Given height (h) = 3.5 m

Volume of hip which is in the form of cone =

$\frac{1}{3} \times \pi \times {r}^{2} \times h \\ \\ \frac{1}{3} \times \frac{22}{7} \times 12 {}^{2} \times 3.5 \\ \\ \frac{1}{3} \times \frac{22}{7} \times 144 \times \frac{7}{2} \\ \\ \frac{1}{3} \times 11 \times 144 \\ \\ 11 \times 48 \\ \\ 528 {m}^{3} \: is \: the \: volume \: of \: rice \: in \: the \: hip$

Now,

Canvas cloth required to cover the hip = Curved Surface area of hip

$curved \: surface \: area \: of \: cone(hip) = \pi \times r \times l$
here, l is slant height

so to find the curved surface area, we need to find the slant height (l)

Therefore,

lt can be found by using Pythagoras theorem

i.e.

${l}^{2} = {r}^{2} + {h}^{2} \\ \\ {l}^{2} = 12 {}^{2} + 3.5 {}^{2} \\ \\ {l}^{2} = 144 + 7 \\ \\ {l}^{2} = 151 \\ \\ l = \sqrt{151} \\ \\ l = \frac{25}{2}$

$therefore \\ \\ curved \: surface \: area \: = \\ \\ \pi \times r \times l \\ \\ \frac{22}{7} \times 12 \times \frac{25}{2} \\ \\ \frac{11}{7} \times 12 \times 25 \\ \\ \frac{3300}{7} \\ \\ 471.42 \: m {}^{2}$

HOPE IT WOULD HELP YOU

Answer 2

Answer:

Since, it is a cone-the volume of cone is:

v=1/3*22/7*12*12*3.5

=527m3Step-by-step explanation:

now, area of canvas required to cover heap=curved surface area of head

∴ C.S.A of cone= 22/7*12*12.5

    Canvas required to cover heap=471m2