Advertisements
Advertisements
Question
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)
Solution
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
RELATED QUESTIONS
In Fig. 5, is a decorative block, made up two solids – a cube and a hemisphere. The base of the block is a cube of side 6 cm and the hemisphere fixed on the top has diameter of 3.5 cm. Find the total surface area of the bock `(Use pi=22/7)`
A solid wooden toy is in the form of a hemisphere surrounded by a cone of same radius. The radius of hemisphere is 3.5 cm and the total wood used in the making of toy is 166 `5/6` cm3. Find the height of the toy. Also, find the cost of painting the hemispherical part of the toy at the rate of Rs 10 per cm2 .[Use`pi=22/7`]
A solid is in the form of a right circular cylinder, with a hemisphere at one end and a cone at the other end. The radius of the common base is 3.5 cm and the heights of the cylindrical and conical portions are 10 cm. and 6 cm, respectively. Find the total surface area of the solid. (Use π =`22/7`)
A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The radius and height of the cylindrical part are 5 cm and 13 cm respectively.The radii of the hemispherical and conical parts are the same as that of the cylindrical part.Find the surface area of the toy if the total height of the toy is 30 cm.
Radii of circular ends of a solid frustum off a cone re 33cm and 27cm and its slant height are 10cm. find its total surface area?
A solid is composed of a cylinder with hemispherical ends. If the length of the whole solid is 108 cm and the diameter of the cylinder is 36 cm, find the cost of polishing the surface at the rate of 7 paise per cm2 .
The volume of a hemisphere is 2425 `1/2` cm3 . Find its curved surface area.
In a village, a well with 10 m inside diameter, is dug 14 m deep. Earth taken out of it is spread all around to a width 5 m to form an embankment. Find the height of the embankment. What value of the villagers is reflected here?
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.
Ramesh made a bird-bath for his garden in the shape of a cylinder with a hemispherical depression at one end. The height of the cylinder is 1.45 m and its radius is 30 cm. Find the total surface area of the bird-bath.
