A toy is in the shape of a solid cylinder surmounted by a conical cap. If the height and diameter of the cylindrical part are 21 cm and 40 cm respectively, and height of the cone is 15 cm , find the total surface area of the toy.

A
$6453.7 c m 2$
B
$5466.37 c m^{2}$
C
$8463.7 c m 2$
D
$4463.6 c m 2$

Solution:

It is given that a toy is in the shape of a solid cylinder surmounted by a conical cap. The height and diameter of the cylindrical part are

21 cm

and

40 cm

respectively. The height of the cone is

15 cm

.
We have to find the required slant height.
Let R and H be the radius and height of the conical top respectively.
Suppose the given terms r and h be the radius and height of the cylindrical part.
As we know the Slant height of the cone,

l = \sqrt{R^{2} + H^{2}}

\Rightarrow l = \sqrt{{(20)}^{2} + {(15)}^{2}}

\Rightarrow l = \sqrt{400 + 225}

\Rightarrow l = \sqrt{625}

\Rightarrow l = 25 cm

Total surface of the toy = Curved surface area of cone + Curved surface area of cylinder + Area of base.
We know that,

Curved surface area of cone = πRl

Curved surface area of cylinder = 2 πrh

Area of base = π r^{2}

Therefore,

Total surface of the toy = πRl + 2 πrh + π r^{2}

Substituing the values,

\Rightarrow Total surface of the toy = π (20 \times 25) + 2 π (20 \times 21) + π (20)^{2}

\Rightarrow Total surface of the toy = π (500) + 2 π (420) + π (400)

\Rightarrow Total surface of the toy = 1740 π

\Rightarrow Total surface of the toy = 1740 \times \frac{22}{7}

\Rightarrow Total surface of the toy = 5466.37 c m^{2}

The total surface area of the toy is

5466.37 c m^{2}

.
Hence, option 2 is the correct answer.

A toy is in the shape of a solid cylinder surmounted by a conical cap. If the height and diameter of the cylindrical part are $21$ cm and $40 cm$ respectively, and height of the cone is $15 cm$ , find the total surface area of the toy.

Solution:

Related content

Company

Support

Courses

More

JEE

NEET

CUET

CBSE

Popular books

NCERT solutions

NCERT exemplar

State Board

Subject

follow us