A solid sphere of radius 15{ cm} is melted ...

ICSE Class X Math 2013 Paper

Question : 33 of 46

Marks: +1, -0

A solid sphere of radius

15\text{ cm}

is melted and recast into solid right circular cones of radius

2.5\text{ cm}

and height

8\text{ cm}

. Calculate the number of cones recast.

Solution:

Radius of a solid sphere,

r=15\text{ cm}

\;\text{Volume of a solid sphere}\;\;=\;\frac{4}{3}\pi r^3

\;=\;\frac{4}{3}\times \pi(15)^3\text{ cm}^3 .

Now, radius of right circular cone

=2.5\text{ cm}

and

\;\text{height, }\; h=8\text{ cm}\; \text{. }\;

Volume of right circular cone

=\;\frac{1}{3}\pi r^2 h

=\;\frac{1}{3}\pi(2. 5)^2\times 8

\therefore

The number of cones

=\;\frac{\;\text{Volume of a sphere}\;}{\;\text{Volume of a cone}\;}

\;=\;\frac{\;\frac{4}{3}\pi \times (15)^3}{\frac{1}{3}\pi(2.5)^2 \times 8}

\;=\;\frac{15\times 15\times 15}{2.5\times 2.5\times 2}

\;=270

Go to Question:

Prev Question

Next Question