The area of the base of a right circular cone is \(\frac{1408}{7} cm^2\) and its height is 6 cm. Taking π = \(\frac{22}{7}\) , the curved surface area of the cone is:
Calculating Cone Radius from Base Area
The area of the base of a right circular cone is given by the formula \( A_{base} = \pi r^2 \), where \( r \) is the radius of the base.
- Given \( A_{base} = \frac{1408}{7} \, cm^2 \) and \( \pi = \frac{22}{7} \).
- Substitute the values into the formula: \( \frac{22}{7} \times r^2 = \frac{1408}{7} \).
- Multiply both sides by 7: \( 22 r^2 = 1408 \).
- Solve for \( r^2 \): \( r^2 = \frac{1408}{22} = 64 \).
- Calculate the radius: \( r = \sqrt{64} = 8 \, cm \).
Finding Cone Slant Height
The slant height (\( l \)) of a right circular cone is related to the radius (\( r \)) and height (\( h \)) by the Pythagorean theorem: \( l^2 = r^2 + h^2 \).
- Given radius \( r = 8 \, cm \) and height \( h = 6 \, cm \).
- Substitute the values: \( l^2 = 8^2 + 6^2 \).
- Calculate \( l^2 \): \( l^2 = 64 + 36 = 100 \).
- Calculate the slant height: \( l = \sqrt{100} = 10 \, cm \).
Calculating Cone Curved Surface Area
The formula for the curved surface area (CSA) of a right circular cone is \( CSA = \pi r l \).
- Using \( \pi = \frac{22}{7} \), \( r = 8 \, cm \), and \( l = 10 \, cm \).
- Substitute the values: \( CSA = \frac{22}{7} \times 8 \times 10 \).
- Calculate the CSA: \( CSA = \frac{22 \times 80}{7} = \frac{1760}{7} \, cm^2 \).
Therefore, the curved surface area of the cone is \( \frac{1760}{7} \, cm^2 \).
Important Questions from Solid Figures
The area of the floor of a cubical room is 192 m 2. The length of the longest rod that can be kept in that room is :
A solid metallic rectangular block of dimensions 112 cm × 44 cm × 25 cm is melted and recast into a cylinder of radius 35 cm. The curved surface area (in cm 2) of the cylinder is: (Take π = 22/7)
If the volume of a cube is 175616 cm 3, what is its side?
The volume of a right circular cone is 1232 cm 3. If the height of the cone is 24 cm, then what will be the radius of its base?
A right triangle contains the right angle between the sides 5 cm and 7 cm. A cone is generated by revolving about the side 5 cm. The volume of this cone is:
