Right Circular Cone Solved Questions
Question 1: Calculate the surface area when the radius and slant height of a right cone arecones 7 inches and 13 inches, respectively. (Use π = 22/7)
Solution:
Given
Radius (r) = 7 inches
Slant Height (l) = 13 inches
We know that,
Surface Area of Right Cone (TSA) = πr(r + l) square units
TSA = 22/7 × 7 × (7 + 13)
= 22 × 20
= 440 sq. in
Hence, the Surface Area of the Right Cone is 440 sq. in.
Question 2: Find the curved surface area of a right cone if its radius is 7 units and its height is 24 units.
Solution:
Given,
Radius (r) = 7 units
Height (h) = 24 units
We know that,
Curved Area of Right Cone (CSA) = πr√(h2 + r2) square units
CSA = (22/7) × 7 × √(242 + 72)
CSA = 22 × √(576 + 49)
CSA = 22 × 25
CSA = 550 square units.
Hence, the Curved Surface Area of the Right Cone is 550 square units.
Question 3: Find the slant height of a right cone if its radius is 21 cm and its curved surface area is 660are sq. cm. (Use π = 22/7)
Solution:
Given,
Radius of Right Cone (r) = 14 cm
Curved Surface Area of Right Cone = 616 sq. cm
Let slant height of the right cone be l
We know that,
Curved Surface Area of Right Cone = πrl square units
660 = (22/7) × 21 × l
66 × l = 660
l = 660/66 = 10 cm
Hence, the slant height of Right Cone is 10 cm.
Question 4: Find the volume of a right cone if its radius is 21 units and its height is 8 units.
Solution:
Given,
Radius (r) = 21 units
Height (h) = 8 units
We know that,
Volume of Right Cone = (1/3) × πr2 × h
= (1/3) × 22/7 × (21)2 × 8
= 3696 unit3
Thus, the Volume of Right Cone is 3696 unit3
Right Circular Cone
A right circular cone is a 3D shape with a circular base and a curved surface that narrows to a point known as the apex or vertex. The cone’s axis is the line connecting the vertex (apex) to the centre (midpoint) of the circular base. This axis is perpendicular to the base, creating a right angle.
The volume formula for a right circular cone is V = (1/3) × πr2h, where:
- r is the radius of the base circle cone
- h is the height of the cone
This formula tells us that the volume of a cone is one-third of the volume of a cylinder with the same radius and height.
Table of Content
- What is a Right Circular Cone?
- Right Circular Cone Definition
- Right Cone vs Oblique Cone
- Properties of a Right Circular Cone
- Surface Area of a Right Cone
- Volume of a Right Circular Cone
- Frustum of a Right Circular Cone
- Equation of Right Circular Cone
- Examples of Right Circular Cone