The radii of three metal spheres are 3 ,cm, 4 | vedclass

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

Question

(D) The volume of a sphere is given by the formula $V = \frac{4}{3} \pi r^3$.Let the radii of the three spheres be $r_1 = 3 \,cm, r_2 = 4 \,cm$,and $r

Vedclass · Accepted Answer

$6$

Vedclass · Answer

(D) The volume of a sphere is given by the formula $V = \frac{4}{3} \pi r^3$.Let the radii of the three spheres be $r_1 = 3 \,cm, r_2 = 4 \,cm$,and $r_3 = 5 \,cm$.The total volume of the three spheres is $V_{total} = \frac{4}{3} \pi (r_1^3 + r_2^3 + r_3^3)$.$V_{total} = \frac{4}{3} \pi (3^3 + 4^3 + 5^3) = \frac{4}{3} \pi (27 + 64 + 125) = \frac{4}{3} \pi (216)$.Let the radius of the new sphere be $R$. Its volume is $V_{new} = \frac{4}{3} \pi R^3$.Since the volume remains conserved,$V_{new} = V_{total}$.$\frac{4}{3} \pi R^3 = \frac{4}{3} \pi (216)$.$R^3 = 216$.$R = \sqrt[3]{216} = 6 \,cm$.

The radii of three metal spheres are $3 \,cm, 4 \,cm$ and $5 \,cm$ respectively. They are melted into a single solid sphere. Find the radius of the new solid sphere (in $cm$).

Similar Questions

The radius and slant height of a conical vessel are $35 \,cm$ and $91 \,cm$ respectively. What is its capacity in litres (in $.8$)?

$A$ storage tank is in the form of a cube. When it is full of water,the volume of water is $15.625 \, m^3$. If the present depth of water is $1.3 \, m$,find the volume of water already used from the tank (in $m^3$).

Find the surface area of a sphere of diameter $3.5\,m$ (in $m^2$).

Find the curved surface area,total surface area and volume of a hemisphere of diameter $42\, cm$.

The lateral surface area of a cube is $256 \, m^2$. The volume of the cube is (in $m^3$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module