The cost of painting the total surface area of a cone at 25 paise per cm is 176. Find the volume of the cone, if its slant height is 25 cm.
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Answer:
Step-by-step explanation:
Answer:
\begin{gathered}cost \: of \: painting \: the \: t.s.a = 25paise \: per \: {cm}^{2} = 176rs. \\ volume = \pi {r}^{2} h \times \frac{1}{3} \\ slant \: height = 25cm \\ t.s.a = \frac{176 \times 100}{25} \\ = 176 \times 4 \\ = 704 {cm}^{2} \\ \ = \pi.r(l + r) \\ 704 = \pi.r(25 + r) \\ \frac{704 \times 7}{22} = r(25 + r) \\ 32 \times 7 = 25r + {r}^{2} \\ 224 = 25r + {r}^{2} \\ = {r}^{2} + 25r - 224 \\ = {r}^{2} + 32r - 7r - 224 \\ = r(r + 32) - 7(r + 32) \\ = (r - 7)(r + 32) \\ r = 7cm \\ {l}^{2} = {h}^{2} + {r}^{2} \\ {25}^{2} - {7}^{2} = {h}^{2} \\ 625 - 49 = {h}^{2} \\ \sqrt{576} = {h}^{2} \\ h = 24cm \\ then \\ \: volum \: o \: cone = \pi {r}^{2} h \times \frac{1}{3} \\ = \frac{22}{7} \times7 \times 7 \times 24 \times \frac{1}{3} \\ 22 \times 7 \times 8 \times 1 \\ = 1232 {cm}^{2} \end{gathered}
costofpaintingthet.s.a=25paisepercm
2
=176rs.
volume=πr
2
h×
3
1
slantheight=25cm
t.s.a=
25
176×100
=176×4
=704cm
2
=π.r(l+r)
704=π.r(25+r)
22
704×7
=r(25+r)
32×7=25r+r
2
224=25r+r
2
=r
2
+25r−224
=r
2
+32r−7r−224
=r(r+32)−7(r+32)
=(r−7)(r+32)
r=7cm
l
2
=h
2
+r
2
25
2
−7
2
=h
2
625−49=h
2
576
=h
2
h=24cm
then
volumocone=πr
2
h×
3
1
=
7
22
×7×7×24×
3
1
22×7×8×1
=1232cm
2