A shot-put iron sphere of diameter 2 cm is melted and cast into a solid cylinder of height 2 cm. What will be the diameter of the cylinder thus made?
A shot-put iron sphere of diameter 2 cm is melted and cast into a solid cylinder of height 2 cm. What will be the diameter of the cylinder thus made?
2 cm व्यास वाले लोहे से बने एक गोले (shot-put) को पिघलाकर 2 cm ऊंचाई वाला एक ठोस बेलन में ढाला जाता हैं इस प्रकार बने बेलन का व्यास क्या होगा?
Detailed Solution & Logic
Correct Answer:
24 cm
Sphere radius = $6$ cm
Sphere volume:
$V = \frac{4}{3}\pi r^3$
$= \frac{4}{3}\pi (6)^3$
$= 288\pi$
Cylinder height = $2$ cm
Let cylinder radius = $R$
Cylinder volume:
$V = \pi R^2 h$
$= \pi R^2 \times 2$
$= 2\pi R^2$
Since volume remains same:
$2\pi R^2 = 288\pi$
$R^2 = 144$
$R = 12$
Diameter of cylinder = $2 \times 12 = 24$ cm
Correct answer: 24 cm
Similar Practice Questions
A cylindrical disc of thickness 1 cm
A cylindrical disc of thickness 1 cm is made by melting two solid cylinders of...
The curved surface area of a of a cylindrical rod is 9900 cm\(^2\). If the length of the rod is 82 cm, find the outer radius of the rod (in cm) correct to two decimal places. Take \(\pi = \frac{22}{7}\).
The curved surface area of a of a cylindrical rod is 9900 cm\(^2\). If the...
AB is a chord of length 32 cm of a circle of radius 20 cm, the tangents at A and B intersect at a point T. Find length TA (rounded off to two digits after decimal).
AB is a chord of length 32 cm of a circle of radius 20 cm,...
A square field has a diagonal of $\surd98$ m. What is its area?
A square field has a diagonal of $\surd98$ m. What is its area? एक वर्गाकार...
A spherical tank is filled with water. The radius of the sphere is 6 meters.
A spherical tank is filled with water. The radius of the sphere is 6 meters....
A circle is inscribed in a right – angled triangle with legs of length 5 and 12.
A circle is inscribed in a right – angled triangle with legs of length 5...
Samriddh has a solid metal ball with a diameter of 9 cm. He melts it and uses the material to make a solid cylinder. If the diameter of the cylinder is the same as that of the ball, find the height of the cylinder.
Samriddh has a solid metal ball with a diameter of 9 cm. He melts it...