Advertisements
Advertisements
Question
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.
Solution
Height of cone = 15 cm
And radius of the base = `7/2` cm
Therefore, volume of the solid = volume of the conical part + volume of hemispherical part.
= `1/3pir^2h + 2/3pir^3`
= `1/3pir^2(h + 2r)`
= `1/3 xx 22/7 xx 7/2 xx 7/2(15 + 2 xx 7/2)`
= `847/3`
= 282.33 cm3
APPEARS IN
RELATED QUESTIONS
A bus stop is barricaded from the remaining part of the road, by using 50 hollow cones made of recycled cardboard. Each cone has a base diameter of 40 cm and height 1 m. If the outer side of each of the cones is to be painted and the cost of painting is ₹ 12 per m2, what will be the cost of painting all these cones?
`("Use "π = 3.14" and take "sqrt1.04= 1.02)`
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.
Find the volume of a right circular cone with:
radius 3.5 cm, height 12 cm
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).
The circumference of the base of a 12 m high conical tent is 66 m. Find the volume of the air contained in it.
The radius and the 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)
Two right circular cone 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.
A solid cone of height 8 cm and base radius 6 cm is melted and recast into identical cones, each of height 2 cm and diameter 1 cm. Find the number of cones formed.
A buoy is made in the form of hemisphere surmounted by a right cone whose circular base coincides with the plane surface of hemisphere. The radius of the base of the cone is 3.5 metres and its volume is two-third of the hemisphere. Calculate the height of the cone and the surface area of the buoy, correct to two places of decimal.
In the following diagram a rectangular platform with a semi-circular end on one side is 22 metres long from one end to the other end. If the length of the half circumference is 11 metres, find the cost of constructing the platform, 1.5 metres high at the rate of Rs. 4 per cubic metres.
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.
The heights of two cones are in the ratio 1:3 and their base radii are in the ratio 3:1. Find the ratio of their volumes.
The curved surface area of a right circular cone of radius 11.3 cm is 710 cm2. What is the slant height of the cone ?
A sphere and a cone have the same radii. If their volumes are also equal, prove that the height of the cone is twice its radius.
A hollow metallic cylindrical tube has an internal radius of 3.5 cm and height 21 cm. The thickness of the metal tube is 0.5 cm. The tube is melted and cast into a right circular cone of height 7 cm. Find the radius of the cone, correct to one decimal place.
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 ratio of the base area and the curved surface of a conical tent is 40: 41. If the height is 18 m, Find the air capacity of the tent in terms of n.
A cone and a hemisphere have equal bases and equal volumes. Find the ratio of their heights.
The circumference of the base of a 10 m high conical tent is 44 metres. Calculate the length of canvas used in making the tent if the width of the canvas is 2m. (Take π = 22/7)
The curved surface area of a right circular cone of height 15 cm and base diameter 16 cm is
