Advertisements
Advertisements
Question
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 the 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.
Solution
We have,
the base radius of none = the base radius of cylinder = the base radius of hemisphe = r= 5 cm,
the total height of the toy = 30 cm
Also, the height of the cone, h=30 - (13 + 5) = 12 cm
The slant height of the cone, `l = sqrt(r^2+ h^2)`
`= sqrt(5^2 + 12^2)`
`= sqrt(25+144)`
`=sqrt(169)`
= 13 cm
Now, the surface area of the toy= CSA of cone +CSA of cylinder + CSA of hemisphere
`= pirl + 2pirH + 2pir^2 `
`=pirl (l + 2H+2r)`
`= 22/7xx5xx(13+2xx13+2xx5)`
`= 22/7xx5xx(13xx26+10)`
`= 22/7xx5xx49`
=770 cm2
So, the surface area of the toy is 770 cm2.
APPEARS IN
RELATED QUESTIONS
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)
From a solid cylinder of height 2.8 cm and diameter 4.2 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid [take 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`]
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 \[\left( r_1^3 + r_2^3 \right)^\frac{1}{3}\].
A solid sphere of radius r is melted and cast into the shape of a solid cone of height r, the radius of the base of the cone is
From a solid cylinder of height 2.8 cm and diameter 4.2 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid.
How many cubes of 10 cm edge can be put in a cubical box of 1 m edge?
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.
The total surface area of a solid hemisphere of radius r is ________.
Tamper-proof tetra-packed milk guarantees both freshness and security. This milk ensures uncompromised quality, preserving the nutritional values within and making it a reliable choice for health-conscious individuals.
500 ml milk is packed in a cuboidal container of dimensions 15 cm × 8 cm × 5 cm. These milk packets are then packed in cuboidal cartons of dimensions 30 cm × 32 cm × 15 cm.
Based on the above-given information, answer the following questions:
i. Find the volume of the cuboidal carton. (1)
ii. a. Find the total surface area of the milk packet. (2)
OR
b. How many milk packets can be filled in a carton? (2)
iii. How much milk can the cup (as shown in the figure) hold? (1)
