Advertisements
Advertisements
Question
Two cones with same base radius 8 cm and height 15 cm are joined together along their bases. Find the surface area of the shape so formed.
Advertisements
Solution
According to the question,
We get the figure given below,
We know that,
Total surface area of shape formed = Curved area of first cone + Curved surface area of second cone
Since, both cones are identical,
We have,
Total surface area of shape formed = Curved area of first cone + Curved surface area of the second cone
= 2(Surface area of cone)
We also know that,
Surface area of cone = πrl, where r = radius and l = slant height
And the total surface area of shape so formed = 2πrl
Given in the question that,
Radius, r = 8 cm
Height, h = 15 cm
Therefore,
Area = Curved area of first cone + Curved surface area of the second cone
= 2(Surface area of the cone)
= 2 × πrl
= `2 xx π xx "r" xx sqrt("r"^2 + "h"^2)`
= `2 xx 22/7 xx 8 xx sqrt(8^2 + 15^2)`
= `50.28 xx sqrt(289)`
= 854.85 cm2
= 855 cm2 ...(Approx)
Hence, the surface area of shape so formed is 855cm2.
APPEARS IN
RELATED QUESTIONS
Due to sudden floods, some welfare associations jointly requested the government to get 100 tents fixed immediately and offered to contribute 50% of the cost. If the lower part of each tent is of the form of a cylinder of diameter 4.2 m and height 4 m with the conical upper part of same diameter but of height 2.8 m, and the canvas to be used costs Rs. 100 per sq. m, find the amount, the associations will have to pay. What values are shown by these associations? [Use π=22/7]
The largest possible sphere is carved out of a wooden solid cube of side 7 em. Find the volume of the wood left. (Use\[\pi = \frac{22}{7}\]).
150 spherical marbles, each of diameter 1.4 cm, are dropped in a cylindrical vessel of diameter 7 cm containing some water, which are completely immersed in water. Find the rise in the level of water in the vessel.
A toy is in the form of a cone of base radius 3.5 cm mounted on a hemisphere of base diameter 7 cm. If the total height of the toy is 15.5 cm, find the total surface area of the top (Use π = 22/7)
A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of Rs 500 per m2.
(Note that the base of the tent will not be covered with canvas.) [Use `pi = 22/7`]
A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in given figure. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the total surface area of the article.
[Use `pi = 22/7`]
From a solid right circular cylinder of height 2.4 cm and radius 0.7 cm, a right circular cone of same height and same radius is cut out. Find the total surface area of the remaining solid.
A bucket has top and bottom diameter of 40 cm and 20 cm respectively. Find the volume of the bucket if its depth is 12 cm. Also, find the cost of tin sheet used for making the bucket at the rate of Rs. 1.20 per dm2 . (Use π = 3.14)
A metallic cylinder has radius 3 cm and height 5 cm. To reduce its weight, a conical hole is drilled in the cylinder. The conical hole has a radius of `3/2` cm and its depth is `8/9 `cm. Calculate the ratio of the volume of metal left in the cylinder to the volume of metal taken out in conical shape.
If r1 and r2 be the radii of two solid metallic spheres and if they are melted into one solid sphere, prove that the radius of the new sphere is \[\left( r_1^3 + r_2^3 \right)^\frac{1}{3}\].
The volume of a hemisphere is 2425 `1/2` cm3 . Find its curved surface area.
A copper wire of diameter 6 mm is evenly wrapped on a cylinder of length 18 cm and diameter 49 cm to cover its whole surface. Find the length and the volume of the wire. If the density of the copper be 8.8 g per cm3, then find the weight of the wire.
A cone of height 24 cm and radius of base 6 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the radius of the sphere and hence find the surface area of this sphere.
Eight solid sphere of same size are made by melting a solid metallic cylinder of base diameter 6 cm and height 32 cm. The diameter of each sphere is ______.
If two solid hemispheres of the same base radius r are joined together along their bases, then curved surface area of this new solid is ______.
A plumbline (sahul) is the combination of (see figure) ______.
The boilers are used in thermal power plants to store water and then used to produce steam. One such boiler consists of a cylindrical part in middle and two hemispherical parts at its both ends.
Length of the cylindrical part is 7 m and radius of cylindrical part is `7/2` m.
Find the total surface area and the volume of the boiler. Also, find the ratio of the volume of cylindrical part to the volume of one hemispherical part.
