If the diameter of a sphere is decreased by 2 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the original diameter be $D$. The radius is $r = D/2$.The surface area of a sphere is $A = 4 \pi r^2 = 4 \pi (D/2)^2 = \pi D^2$.If the diamete

Vedclass · Accepted Answer

$43.75$

Vedclass · Answer

(C) Let the original diameter be $D$. The radius is $r = D/2$.The surface area of a sphere is $A = 4 \pi r^2 = 4 \pi (D/2)^2 = \pi D^2$.If the diameter is decreased by $25 \%$,the new diameter $D' = D - 0.25D = 0.75D$.The new surface area $A' = \pi (D')^2 = \pi (0.75D)^2 = 0.5625 \pi D^2$.The decrease in surface area is $A - A' = \pi D^2 - 0.5625 \pi D^2 = 0.4375 \pi D^2$.The percentage decrease is $\frac{0.4375 \pi D^2}{\pi D^2} 	imes 100 \% = 43.75 \%$.

If the diameter of a sphere is decreased by $25 \%$,its curved surface area will be decreased by (in $\%$).

Similar Questions

$A$ cone and a cylinder having the same area of the base have also the same area of curved surfaces. If the height of the cylinder is $2 \, m$,find the slant height of the cone (in $m$).

The outer dimensions of a closed box are $12 \text{ cm}$ by $10 \text{ cm}$ by $8 \text{ cm}$. If the box is made of wood $1 \text{ cm}$ thick,find out the capacity of the box (in $\text{cm}^3$).

$A$ solid sphere and a solid hemisphere have the same total surface area. The ratio of their volumes is

The volumes of two cubes are in the ratio of $8: 125$. Find the ratio of their edges and surface areas.

The total surface area of a hemisphere is $41.58 \text{ cm}^2$. Find its curved surface area (in $\text{cm}^2$).

Vedclass Test Series

Exam Paper Generator

Online Exam Module