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{...

### The curved surface area of a cone is 12320 cm2. If the radius of its base is 56 cm, find its height.

Curved surface area of the cone = 12320 cm2 Radius of the base = 56 cm Let the slant height be ‘l’ Curved surface area \[\begin{array}{*{35}{l}} =\text{ }\pi rl\text{ }=\text{ }12320\text{...

### Find the volume of a cone whose slant height is 17 cm and radius of base is 8 cm.

Slant height of the cone (l) = 17 cm Base radius (r) \[\begin{array}{*{35}{l}} =\text{ }8\text{ }cm \\ {{l}^{2}}~=\text{ }{{r}^{2}}~+\text{ }{{h}^{2}} \\ {{h}^{2}}~=\text{ }{{l}^{2}}~-\text{...