Question
A shot-put made of iron with a diameter of 12 cm is melted into a solid cylinder with a height of 2 cm. What is the diameter of the cylinder made?
The correct answer is
24 cm
Volume of the shot-put (sphere) = (4/3) × π × (6³)
= (4/3) × π × 216 = 288π cm³
Volume of the cylinder = π × r² × h
288π = π × r² × 2
r² = 144
r = 12 cm
Diameter of the cylinder = 2 × 12 = 24 cm
Thus, the correct answer is 24 cm.
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Important Questions from Mensuration
- The volume of a wall that is 5 times as high as it is broad and 8 times as long as it is high is 12.8 cubic meters. Find the breadth of the wall.
- If the radius of a sphere is increased by 2 cm, then its surface area increases by 704 cm\(^2\). Using \(\pi = \frac{22}{7}\), find the radius of the sphere after the increase.
- What is the perimeter of an equilateral triangle with side 13 cm?
- The perimeter of a square is 76 m. Its area (in $m^2$) is:
- A cylindrical rod has an outer curved surface area of 1800 cm$^2$. If the length of the rod is 52 cm, then the outer radius (in cm) of the rod, correct to two places of decimal, is:
Take $\pi = \frac{22}{7}$
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