Question

If a solid sphere of radius r is melted and cast into the shape of a solid cone of height r, then the radius of the base of the cone is
A. 2r
B. 3r
C. r
D. 4r

Answer 1

Answer:

options (c) r will be the right answer

Answer 2

The radius of the base of the cone is 2r. Option A is correct.

Step-by-step explanation:

• Given data

        Radius of sphere $\mathbf{(R_{s})=r}$

        Height of cone (H) = r

        Let radius of cone $\mathbf{(R_{c})=R}$

• From formula of volume of sphere

        Volume of sphere $\mathbf{(V_{s})=\frac{4}{3}\pi R_{s}^{3}}$        ...1)

• From formula of volume of cone

        Volume of cone $\mathbf{(V_{c})=\frac{1}{3}\pi R_{c}^{2}H}$       ...2)

• Given that sphere is cast into cone, so

        Volume of cone = Volume of sphere

        $\mathbf{\frac{1}{3}\pi R_{c}^{2}H=\frac{4}{3}\pi R_{s}^{3}}$

        On cancel out common term on both side, we get

        $\mathbf{R_{c}^{2}H=4\times R_{s}^{3}}$    

• On putting respective value in above equation, we get

        $\mathbf{R_{c}^{2}\times r=4\times r^{3}}$

       On cancel out common term on both side, we get

        $\mathbf{R_{c}^{2}=4\times r^{2}}$

        So

        $\mathbf{R_{c}=2r}$ = This is base radius of cone.