Advertisements
Advertisements
प्रश्न
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)
Advertisements
उत्तर
Let r and h be the radius and height of the cone mounted on the hemisphere, respectively.
Suppose R be the radius of the hemishpere.
Now,
r = R = 3.5 cm
Height of the cone + Radius of the hemisphere = Total height of the toy
∴ h + 3.5 cm = 15.5 cm
⇒ h = 15.5 − 3.5 = 12 cm
Let l be the slant height of the cone.
∴l2=r2+h2
`=>l^2=(7/2)^2+(12)^2=49/4+144=625/4`
`=>l = 25/2cm`
Total surface area of the toy
= Curved surface area of the cone + Curved surface area of the hemisphere
=πrl+2πr2
=πr(l+2r)
`=22/7xx7/2xx(25/2+2xx7/2)`
`=22/7xx7/2xx39/2`
=214.5 cm2
APPEARS IN
संबंधित प्रश्न
504 cones, each of diameter 3.5 cm and height 3 cm, are melted and recast into a metallic sphere. Find the diameter of the sphere and hence find its surface area.
[Use π=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 vessel is in the form of hemispherical bowl surmounted by a hollow cylinder of same diameter. The diameter of the hemispherical bowl is 14 cm and the total height of the vessel is 13 cm. Find the total surface area of the vessel. `[\text{Use}pi=22/7]`
A solid sphere of radius 'r' is melted and recast into a hollow cylinder of uniform thickness. If the external radius of the base of the cylinder is 4 cm, its height 24 cm and thickness 2 cm, find the value of 'r'.
Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of hemisphere?
A right triangle whose sides are 15 cm and 20 cm (other than hypotenuse), is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed. (Choose value of π as found appropriate)
The volume of a hemisphere is 19404 cm3. The total surface area of the hemisphere is
A plumbline (sahul) is the combination of (see figure) ______.
Two identical solid hemispheres of equal base radius r cm are stuck together along their bases. The total surface area of the combination is 6πr2.
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.
