In a manufacturing plant, a cone-shaped part has a curved surface area of 330 cm² and a base radius of 7 cm. What is its height?
13.26 cm
Given: a cone with curved (lateral) surface area 330 cm² and base radius 7 cm. We must find its vertical height.
The curved surface area of a cone is \(\text{CSA} = \pi r l\), where \(l\) is the slant height.
Substituting known values: \(330 = \dfrac{22}{7} \times 7 \times l\).
Simplifying: \(330 = 22 l\), so \(l = \dfrac{330}{22} = 15 \text{ cm}\).
The slant height, radius and height satisfy \(l^2 = r^2 + h^2\), hence \(h = \sqrt{l^2 - r^2}\).
Substituting: \(h = \sqrt{15^2 - 7^2} = \sqrt{225 - 49} = \sqrt{176}\).
This gives \(h \approx 13.27 \text{ cm}\), matching the option. Hence the height is 13.26 cm.
Similar Questions
An ice cream cone has a radius of 2 cm and slant height of 5 cm. If 100 such cones are to be painted externally (excluding base), what is the total painted area?
A manufacturer reduces the diameter of their spherical bearing balls by 50% to cut costs. What is the percentage decrease in volume of each ball?
A small temple dome is shaped like a hemisphere of radius 3.5 m. How much area (in square meters) must be painted on the curved surface?
A sphere is tightly enclosed inside a cube of side length a. If the cube is then inscribed inside another sphere, what is the ratio of the inner to outer sphere volumes?
A right circular cone has a height of 12 cm and a radius of 5 cm. Find its slant height and curved surface area.
A solid metallic sphere of radius R is heated so that its radius increases by 10%. Find the approximate percentage increase in its volume.
Two identical regular right pyramids, each with a square base of side 6 cm and a perpendicular height of 4 cm, are stacked one on top of the other such that their bases perfectly align. The top pyramid is inverted. Calculate the slant height of a single pyramid.
The base of a regular right pyramid is an isosceles triangle with equal sides of 25 cm and a base of 30 cm. The slant height of the pyramid is 40 cm. Find the total surface area of the pyramid.
If the lateral surface area of a right circular cylinder is equal to twice the area of its base, find the height in terms of the radius.
If the surface area of a sphere increases by 44%, by what approximate percent does the radius increase?
Important Questions from Solid Figures
A cone and a hemisphere have equal bases and volumes. What is the ratio of the height of the cone to the radius of the hemisphere?
If the surface area of a sphere is 64 π cm 2, then the volume of the sphere is:
Find the surface area of a sphere of diameter 21 cm. (Use π = \(\frac{{22}}{7}\) )
A cube is 7 cm of an edge and another cube is 14 cm on an edge. The ratios of their surface areas are
Using three distinct points which of the following shapes cannot be formed?
