The radius of a cylinder is 10, cm and its he | vedclass

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

Question

(A) Let the radius be $r = 10\, cm$ and the height be $h = 4\, cm$.Let the value added to either the radius or the height be $x\, cm$.Case $1$: When $

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(A) Let the radius be $r = 10\, cm$ and the height be $h = 4\, cm$.Let the value added to either the radius or the height be $x\, cm$.Case $1$: When $x$ is added to the radius,the new radius is $(10+x)\, cm$ and the height remains $4\, cm$.The new volume $V_1 = \pi(10+x)^2 	imes 4$.Case $2$: When $x$ is added to the height,the radius remains $10\, cm$ and the new height is $(4+x)\, cm$.The new volume $V_2 = \pi(10)^2 	imes (4+x)$.According to the problem,the increase in volume is the same,which implies $V_1 = V_2$ (since the original volume is subtracted from both sides,the net increase is equal if the final volumes are equal).$\pi(10+x)^2 	imes 4 = \pi(10)^2(4+x)$$(10+x)^2 	imes 4 = 100(4+x)$$4(100 + 20x + x^2) = 400 + 100x$$400 + 80x + 4x^2 = 400 + 100x$$4x^2 - 20x = 0$$4x(x - 5) = 0$Since $x$ cannot be $0$,we have $x = 5\, cm$.

The radius of a cylinder is $10\, cm$ and its height is $4\, cm$. The value of $x$ (in $cm$) that may be added either to the radius or to the height to get the same increase in the volume of the cylinder is:

Similar Questions

$A$ reservoir, $30\, m$ long and $15\, m$ broad, is filled with water. How many gallons of water must be taken out to lower the level of water by $4\, m$? (in gallons)

$A$ cylinder with base radius of $8\, cm$ and height of $2\, cm$ is melted to form a cone of height $6\, cm.$ The radius of the cone will be (in $cm$):

The ratio of the curved surface area and volume of a cylinder is $1:7$. The ratio of the total surface area and volume is $187:770$. What is the ratio of its base radius to its height?

$10$ identical solid spherical balls of radius $3 \text{ cm}$ are melted to form a single sphere. In this process,$20 \%$ of the solid is wasted. What is the radius (in $\text{cm}$) of the resulting sphere?

$A$ solid cylinder has a base radius of $14\, cm$ and a height of $15\, cm$. Identical small cylinders are cut from each base as shown in the figure. The height of each small cylinder is $5\, cm$ and the radius is $7\, cm$. What is the total surface area (in $cm^2$) of the remaining part?

Vedclass Test Series

Exam Paper Generator

Online Exam Module