How much percent of the curved surface area of a sphere will be increased if the radius is doubled?
WBBSE
Class X
Mathematics
Sphere
02 Mark
2024
Curved surface area (C.S.A) of a sphere = 4πr²
If radius is doubled
⇒ new radius = 2r.
New C.S.A = 4π(2r)² = 4π × 4r² = 16πr².
Increase in C.S.A = (New C.S.A − Old C.S.A)
= 16πr² − 4πr² = 12πr²
% increase = (Increase C.S.A / Old C.S.A) × 100
= (12πr² / 4πr²) × 100
= 300%.
Related Questions
More WBBSE Moderate level questions
1/12
Q.
The numerical value of the volume of a sphere is twice the numerical value of...
A.
Volume of the sphere = πr³ Surface area of the sphere =...
Q.
If the length of the radius of a sphere is increased by 50%, find how...
A.
Original radius = r (let) New radius = 1.5 r Original Surface...
Q.
Melting a solid Lead sphere of diameter 12 cm, three small solid spheres are made....
A.
Radius of Lead sphere (R) = = 6 cm Volume of Lead...
Q.
Two solid spheres with radii of 1 cm and 6 cm lengths are melted and...
A.
Volume of sphere = πr³ Total volume of two sphere = π(1³...
Q.
State True or False: If the numerical values of the curved surface area and volume...
A.
True Explanation CSA of sphere = Volume of Sphere 4πr² = πr³...
Q.
Calculate how many spherical marbles with 1 cm radius each may be formed by melting...
A.
Radius of big sphere = 8 cm Radius of each marble =...
Q.
State True or False: The ratio of whole surfaces of a solid sphere and a...
A.
False Explanation: Whole surface of sphere = 4πr². Whole surface of hemisphere...
Q.
The greatest volume of a solid cone which can be cut off from a solid...
A.
(2/3)πr³ Explanation: The largest cone that can be cut from a hemisphere...
Q.
If the ratio of the volumes of two solid spheres is 27 : 8, then...
A.
(b) 9 : 4 Explanation Given ratio of volumes = 27 :...
Q.
What is the name of the solid which is composed of only one surface?
A.
Sphere Explanation: A sphere has one continuous curved surface with no edges...
Q.
If radius of a sphere is r and volume v, then v ∝ ___.
A.
r³ Explanation: Volume of a sphere = πr³. Hence v is directly...
Q.
The volume of a solid sphere having radius 2r units is
A.
(a) r³ cm³ Explanation: V = π(2r)³ = π × 2 ×...