Answer :
Answer:
is given that the volume of a right circular cone is 9856 cm³. If the diameter of the base is 28 cm, we have found that the height of the cone is 48 cm, the slant height of the cone is 50 cm and the curved surface area of the cone is 2200 cm².
Answer:
To find the height of the cone, we can use the formula for the volume of a cone:
\[ V = \frac{1}{3} \pi r^2 h \]
Given that the diameter of the base is 28 cm, the radius (r) is half of that, so \( r = \frac{28}{2} = 14 \) cm.
Substituting the known values into the volume formula:
\[ 9856 = \frac{1}{3} \times \frac{22}{7} \times 14^2 \times h \]
Solving for \( h \):
\[ h = \frac{3 \times 9856}{22 \times 14^2} \]
\[ h ≈ \frac{3 \times 9856}{22 \times 196} \]
\[ h ≈ \frac{29568}{4312} \]
\[ h ≈ 6.85 \, \text{cm} \]
So, the height of the cone is approximately 6.85 cm.
To find the slant height (l), we can use the Pythagorean theorem, since the slant height, the radius, and the height form a right triangle:
\[ l = \sqrt{r^2 + h^2} \]
\[ l = \sqrt{14^2 + 6.85^2} \]
\[ l = \sqrt{196 + 46.9225} \]
\[ l ≈ \sqrt{242.9225} \]
\[ l ≈ 15.57 \, \text{cm} \]
So, the slant height of the cone is approximately 15.57 cm.
To find the curved surface area (CSA) of the cone, we can use the formula:
\[ CSA = \pi r l \]
\[ CSA ≈ \frac{22}{7} \times 14 \times 15.57 \]
\[ CSA ≈ 22 \times 2.22 \]
\[ CSA ≈ 48.84 \, \text{cm}^2 \]
So, the curved surface area of the cone is approximately 48.84 cm².
Step-by-step explanation:
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