Question
A right circular cone of height h and radius R is cut by a plane parallel to the base at a distance h/4 from the base. The ratio of the curved surface areas of the resulting cone to the frustum is:
The correct answer is
9 : 7
Height of the smaller cone = h - (h/4) = (3h/4)
By similarity, ratio of radii = (3h/4) : h = 3:4
Curved surface area (CSA) ratio of smaller cone to original cone = (3²) : (4²) = 9:16
CSA of frustum = CSA of original cone - CSA of smaller cone
Ratio of smaller cone to frustum = 9 : (16 - 9) = 9 : 7
Thus, the correct answer is 9 : 7.
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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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