The volume of a right circular cone is 9856cm2. If diameter of the base is 28cm. Find a) Height of the cone. b) Slant height.
c)Curved surface area. d)Total surface area
Answers
Answer:
Given−
\blue{\texttt{volume \: of \: a \: right \: circular \: cone \: is }}volume of a right circular cone is 9856 {cm}^{2} 9856cm
2
\blue{\texttt{diameter \: of \: the \: base \: is }}diameter of the base is 28cm .
so \: \: r = \large\frac{28}{2} sor=
2
28
= 14 cm
\underline\blue{\bold{To \: Find }}
ToFind
:-
a) Height of the cone.
b) Slant height.
c)Curved surface area
d)Total surface area.
\red{\textbf{(i)height}}(i)height = \underline\blue{\bold{h}}
h
\red{\textbf{volume}}volume =
9856 = \large \frac{1}{3} \pi {r}^{2} h9856=
3
1
πr
2
h
9856 = \frac{1}{3} \times \frac{22}{7} \times 14 \times 14 \times h9856=
3
1
×
7
22
×14×14×h
h = 48 \: cmh=48cm
\red{\textbf{(ii) \: slant \: height}}(ii) slant height =
{l}^{2} = \sqrt{ {r}^{2} + {h}^{2} } l
2
=
r
2
+h
2
{l}^{2} = \sqrt{ {14}^{2} + {48}^{2} } = \sqrt{196 + 2304} l
2
=
14
2
+48
2
=
196+2304
{l }^{2} = 2500l
2
=2500
l = \sqrt{2500} l=
2500
l = \sqrt{(5 {0)}^{2} } l=
(50)
2
l \: = 50 \: cml=50cm
\red{\textbf{(iii) \: curved \: surface \: Area}}(iii) curved surface Area =>
we know that r = 14 cm and l = 50cm
(\pi \: rl \: = \large \frac{22}{7} \times 14 \times 50) {cm}^{2} (πrl=
7
22
×14×50)cm
2
= (22 \: \times 2 \times 50)c {m}^{2} =(22×2×50)cm
2
= 2200 \: c {m}^{2} =2200cm
2
\red{\textbf{(iv) \: total \: surface \: area}}(iv) total surface area = πr(l + r)
= 22/7 × 14(50 + 14)
= 22 × 2(64)
= 22 × 2 × 64
= 8192 \: c {m}^{2} =8192cm
2
•\blue{\texttt{height \: of \: cone}}height of cone 14cm
•\blue{\texttt{slant \: height \:}}slant height 50 {cm}^{2} 50cm
2
•\blue{\texttt{curved \: surface \: area}}curved surface area 2200 {cm}^{2} 2200cm
2
•\blue{\texttt{total \: surface \: area}}total surface area 8192 \: c {m}^{2} 8192cm
2
this answer for your first question