the perpendicular height of a. cone is 35cm and its volume is2970cu.cm find the diameter of the base
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the perpendicular height of a. cone is 35cm and its volume is2970cu.cm find the diameter of the base
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Answer:
Let r and l be the radius and the slant height of the solid right circular cone respectively.
r=35cm,l=37cm
Curved Surface area, CSA=πrl=π(35)(37)
CSA=4070sq.cm
Total surface area, TSA=πr(l+r)
=
7
22
×35×(37+35)
Thus, TSA=7920sq.cm
S O L U T I O N :
[tex]\underline{\bf{Given\::}}[/tex]
[tex]\underline{\bf{Explanation\::}}[/tex]
As we know that formula of the volume of cube;
[tex]\boxed{\bf{Volume= \frac{1}{3} \pi r^{2}h\:\:(cubic\:unit)}}[/tex]
A/q
[tex]\mapsto\tt{2970 = \dfrac{1}{3} \times \dfrac{22}{\cancel{7}} \times r^{2} \times \cancel{35}}[/tex]
[tex]\mapsto\tt{2970 = \dfrac{1}{3} \times 22 \times r^{2}\times 5}[/tex]
[tex]\mapsto\tt{2970 \times 3 =110\times r^{2}}[/tex]
[tex]\mapsto\tt{8910 = 110\times r^{2}}[/tex]
[tex]\mapsto\tt{r^{2} = \cancel{\dfrac{8910}{110} }}[/tex]
[tex]\mapsto\tt{r^{2} = 81}[/tex]
[tex]\mapsto\tt{r = \sqrt{81} }[/tex]
[tex]\mapsto\bf{r= 9\:cm}[/tex]
So, radius of the cone is 9 cm.
As we know that diameter of cone;
→ Diameter of cone = 2 × radius
→ Diameter of cone = 2 × 9 cm
→ Diameter of cone = 18 cm .