Surface Area of Composite Figures

Concept Explanation

Surface Area of Composite Figures

Composite Figure: A figure that can be divided into more than one of the basic figures is known as Composite figure(Shape).

Illustration: A solid wooden toy is in the shape of a right circular cone mounted on a hemisphere. If the radius of the hemisphere is 7cm and the total height of the toy is 31 cm, find the surface area of the wooden toy.

Solution: Let r be the radius of the hemisphere and h be the height of the conical part of the toy. Then,

r = 7cm , height of cone = (31 - 7 ) cm = 24 cm.

Also, radius of the base of the cone = 7 cm

Slant height of cone = $sqrt{h^2+r^2}=sqrt{24^2+7^2}=sqrt{576 + 47}=sqrt{625}=25cm$

$large therefore$ Surface Area of Composite Figure = CSA of cone + CSA of hemisphere = $large pi r l + 2pi r^2$

= $large frac{22}{7}times 7times 25 + 2times frac{22}{7}times 7 times 7$

$large =22 times 25 + 2times 22 times 7$

= 550 + 308

= $large 858cm^2$

Illustration: A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The height and radius of the cylindrical part are 13 cm and 5 cm respectively. The radii of the hemispherical and conical parts are the same as that of the cylindrical part. Calculate the surface area of the toy if height of the conical part is 12 cm.

Solution: Let r cm the radius and h cm the height of the cylindrical part. Then,

r = 45 cm and h = 13 cm

Radii of the spherical part and base of the conical part are also r cm. Let $large h_{1}$ cm be the height, l cm be the slant height of the conical part. Then,

$l^{2}=r^{2}+h_{1}^{2}$

$Rightarrow l=sqrt{r^{2}+h_{1}^{2}}$

$Rightarrow l=sqrt{5^{2}+(12)^{2}}$

$Rightarrow l=sqrt{169}$

$Rightarrow l=13;cm$

Now, Surface area of the toy = Curved Surface area of the cylindrical part + Curved Surface Area of hemispherical part + Curved Surface Area conical part

$=(2pi rh+2pi r^{2}+pi rl);cm^{2}$

$=pi r(2h+2r+l);cm^{2}$

$=frac{22}{7}times 5times(2times 13+2 times5+13);cm^{2}$

$=frac{22}{7}times 5times(49);cm^{2}$

$=770;cm^{2}$

Sample Questions

(More Questions for each concept available in Login)

Question : 1

A storage tank consists of a circular cylinder, with a hemisphere adjoined on either end. If the external diameter of the cylinder be 1.4 m and its length be 5m, what will be the cost of painting it on the outside at the rate of Rs 10 per square meter?
A. 281.60	B. 280.56	C. 281.51	D. 281.66
Right Option : A
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Question : 2

Find the surface area of the following composite figure. Use $pi = 3.14$
A. 637.42 sq units	B. 367.42 sq units	C. 363.42 sq units	D. 673.42 sq units
Right Option : A
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Question : 3

A storage tank consists of circular cylinder with a hemisphere adjoining at either end. If the diameter of the cylinder be 1.4 m and its length be 8 m, the cost of painting it on the outside at the rate of Rs 10 per m2 will be _______________
A. Rs 398.2	B. Rs 41.36	C. Rs 413.88	D. Rs 382.80
Right Option : A
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