Right Circular Cone

Multiple Choice Questions (MCQ)

1. What is the formula to calculate the slant height (l) of a right circular cone?
A) l = r + h
B) l = r2+h2
C) l = r2-h2
D) l = 13πr2h
Answer: B) l = r2+h2

2. If the radius r = 3 cm and slant height l = 5 cm, what is the curved surface area (CSA)?
A) 15π cm2
B) 30π cm2
C) 12π cm2
D) 24π cm2
Answer: A) 15π cm2

3. The total surface area (TSA) of a cone is given by which of the following?
A) πr2h
B) πrl
C) πr(l+r)
D) 2πrh
Answer: C) πr(l+r)

4. A cone has height h=4h = 4h=4 cm and radius r=3r = 3r=3 cm. What is its volume?
A) 36π cm3
B) 12π cm3
C) 24π cm3
D) 18π cm3
Answer: B) 12π cm3

5. In a cone, if the slant height l=10l = 10l=10 cm and height h=6h = 6h=6 cm, what is the radius?
A) 4 cm
B) 6 cm
C) 8 cm
D) 10 cm
Answer: C) 8 cm

Short Answer Questions (SAQ)

1. Define a right circular cone.
Answer: A right circular cone is a 3D figure with a circular base and a vertex directly above the center of the base. The line from the vertex to the center is perpendicular to the base.

2. Write the formula for the volume of a cone.
Answer: Volume of a cone = 13πr2h

3. If the curved surface area (CSA) of a cone is 80π cm2 and slant height l = 10 cm, find the radius.
Answer: Using curved surface area = πrl,
80π=π×r×10
⇒ r=8 cm

Long Answer Questions (LAQ)

1. A cone has a height of 6 cm and a slant height of 10 cm.
Find: (i) Radius, (ii) Curved Surface Area, (iii) Volume
Answer: (i) Radius: r =l2-h2 = 100 -36 = 64 =8cm
(ii) Curved Surface Area = πrl = π × 8 × 10 = 80π cm2
(iii) Volume = 13πr2h=13π×64×6=128π cm3

2. A cone has radius 3 cm and height 4 cm.
Find: (i) Slant Height, (ii) Total Surface Area, (iii) Volume
Answer: (i) Slant Height l = l2+h2 = 9+16 = 25 = 5cm
(ii) Total Surface Area = πr(l+r) = π × 3 × (5+3) = 24π cm2
(iii) Volume = 13πr2h=13π×9×4=12π cm3

Right Circular Cone