ICOME
    FOLLOW US: facebook twitter instagram youtube
JOIN ICOME
JOIN ICOME
JOIN ICOME

Cones

Theory and Formula


Question


Q1. Height of right circular cone is constant but its radius increased by 10% . Find the increase in volume(in percentage).

(a) 21% (b) 16% (c) 19% (d) 24%

Solution.
(a) 21%
Solution

Q2. Radius and volume of a cone and sphere are same , find the ratio of diameter of sphere and height of cone .

(a) 1:6 (b) 4:1 (c) 1:2 (d) 1:3

Solution.
(c) 1:2
Solution

Q3. The radius and the height of a cone are each increased by 20%, find the percentage increase in volume .

Solution.
72.8%
Solution

Q4. If the height of two cone are in the ratio 1:8 and their diameter are in the ratio 4:5. What is the ratio of their volumes.

Solution.
Ratio of volume = (ratio of radii)2 x ratio of height

16/25
x
1/8
= 2:25
Solution

Q5. Two cones have their heights in the ratio 1:9 and radii 3:1. What is the ratio of their volumes?

Solution.
1:1, both cones have same volume.
Solution

Q6. For the same height and base radius, volume of cylinder will __________ times, the volume of cone.

(a) 2 (b) 1 (c) 4 (d) 3

Solution.
(d) 3
Volume of cylinder = πr2h
Volume of cone = 1/3 πr2h
Solution

Q7. Find the volume of a cone having radius of the base as 30 cm and its slant height as 50 cm
(use π = 3.14)

(a) 49160 cm3 (b) 9980 cm3 (c) 1100 cm3 (d) 37680cm3

Solution.
r = 30 cm
l = 50 cm
h = √l2 - r2 = 40 cm
Volume of cone is = 1/3πr2h
= 37680cm3
Solution

Q8. A right circular cone is 50m high and its base radius is 10m. It is melted and recast into a right circular cone with radius of its base is 5m. Find the height of new cone.

Solution.
Volume of cone = 1/3Πr2h

1/3Πr12h1 = 1/3Πr22h2

r12h1 = r22h2

h2 = (r12h1 )/r22

h2 = (100 x 50)/25 = 200m
Solution

Q9. The radii of the bases of a cylinder and a cone are in the ratio 3:4 and their heights are in the ratio 2:3. What is the ratio of their volumes?

Solution.
9:8
Solution

Q10. A cone and a hemisphere have equal bases. If their height are also equal then what is the ratio of their curved surface ?

(a) √2 : 3 (b) 1: √2 (c) 1 : 1 (d) 1 : 3

Solution.
(b) 1: √2
Solution