Exercise 20B

### There are two cones. The curved surface area of one is twice that of the other. The slant height of the latter is twice that of the former. Find the ratio of their radii.

Let slant height of the first cone = l So, the slant height of the second cone = 2l Radius of the first cone = r1 And, the radius of the second cone = r2 Curved surface area of first cone = πr1l...

### The diameters of two cones are equal. If their slant heights are in the ratio 5:4, find the ratio of their curved surface areas.

Let radius of each cone = r Given that, ratio between their slant heights = 5: 4 Let slant height of the first cone = 5x And slant height of second cone = 4x So, curved surface area of the first...

### Two right circular cones x and y are made, x having three times the radius of y and y having half the volume of x. Calculate the ratio between the heights of x and y.

Let radius of cone y = r radius of cone x = 3r volume of cone y = V Then, volume of cone x = 2V Let h1 be the height of x and h2 be the height of y. \[\begin{array}{*{35}{l}} Volume\text{ }of\text{...

### The radius and height of a right circular cone are in the ratio 5:12 and its volume is 2512 cubic cm. Find the radius and slant height of the cone. (Take π = 3.14)

The ratio between radius and height = 5: 12 Volume of the right circular cone = 2512 cm3 Let its radius (r) = 5x, its height (h) = 12x and slant height = l \[\begin{array}{*{35}{l}}...

### The circumference of the base of a 12 m high conical tent is 66 m. Find the volume of the air contained in it.

Circumference of the base (c) = 66 m Height of the conical tent (h) = 12 m Radius \[=\text{ }c/2\pi \text{ }=\text{ }66/\text{ }2\pi \text{ }=\text{ }\left( 33\text{ x }7 \right)/22\text{ }=\text{...