Advertisements
Advertisements
Question
The curved surface area of a cone is 12320 cm2. If the radius of its base is 56 cm, find its height.
Solution
Curved surface area = 12320 cm2
Radius of base (r) = 56 cm
Let slant height = l
∴ πrl = 12320
`=> 22/7 xx 56 xx l = 12320`
`=> l = (12320 xx 7)/(56 xx 22)`
`=>` l = 70 cm
Height of the cone
= `sqrt(l^2 - r^2)`
= `sqrt((70)^2 - (56)^2 `
= `sqrt(4900 - 3136)`
= `sqrt(1764)`
= 42 cm
APPEARS IN
RELATED QUESTIONS
The radius of a cone is 5 cm and vertical height is 12 cm. Find the area of the curved surface.
The radius and slant height of a cone are In the ratio of 4 : 7. If its curved surface area is 792 cm2, find its radius. (Use it 𝜋 = 22/7).
There are two cones. The curved surface area of one is twice that of the other. The slant height of the later is twice that of the former. Find the ratio of their radii.
Two cones have their heights in the ratio 1 : 3 and the radii of their bases in the ratio 3 : 1. Find the ratio of their volumes.
The radius and the height of a right circular cone are in the ratio 5 : 12. If its volume is 314 cubic meter, find the slant height and the radius (Use it 𝜋 = 3.14).
Find the volume of a cone whose slant height is 17 cm and radius of base is 8 cm.
The volume of a conical tent is 1232 m3 and the area of the base floor is 154 m2. Calculate the:
- radius of the floor,
- height of the tent,
- length of the canvas required to cover this conical tent if its width is 2 m.
A cone of height 15 cm and diameter 7 cm is mounted on a hemisphere of same diameter. Determine the volume of the solid thus formed.
A cubical block of side 7 cm is surmounted by a hemisphere of the largest size. Find the surface area of the resulting solid.
A cone and a hemisphere have the same base and the same height. Find the ratio between their volumes.
The cross-section of a railway tunnel is a rectangle 6 m broad and 8 m high surmounted by a semi-circle as shown in the figure. The tunnel is 35 m long. Find the cost of plastering the internal surface of the tunnel (excluding the floor) at the rate of Rs. 2.25 per m2.
A solid, consisting of a right circular cone standing one a hemisphere, is placed upright in a right circular cylinder, full of water, and touches the bottom. Find the volume of water left in the cylinder, having given that the radius of the cylinder is 3 cm and its height is 6 cm; the radius of
the hemisphere is 2 cm and the height of cone is 4 cm. Give your answer to the nearest cubic centimeter.
Find the curved surface area of a cone whose height is 8 cm and base diameter is 12 cm .
Find the height of the cone whose base radius is 5 cm and volume is 75π cm3.
The total surface area of a right circular cone of slant height 13 cm is 90π cm2. Calculate: its volume in cm3. Take π = 3.14
The internal and external diameters of a hollow hemi-spherical vessel are 21 cm and 28 cm respectively. Find: total surface area.
The surface area of a solid sphere is increased by 21% without changing its shape. Find the percentage increase in its: volume
A conical tent is accommodate to 11 persons each person must have 4 sq. metre of the space on the ground and 20 cubic metre of air to breath. Find the height of the cone.
A cloth having an area of 165 m2 is shaped into the form of a conical tent of radius 5 m. Find the volume of the cone.
