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Mathematics · Surface Areas and Volumes · NCERT Examples

Example 3

A complete, independently verified solution for NCERT Example 3.

Mathematics · Chapter 12 · NCERT Examples

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Verified NCERT questions and solutionsSolutions are checked independently and follow the supplied NCERT chapter edition.

NCERT Example

Example 3

rocket · painted surface area

A wooden toy rocket is a cone mounted on a cylinder. Its total height is 26 cm, the conical part is 6 cm high, the cone diameter is 5 cm and the cylinder diameter is 3 cm. Find the areas painted orange on the cone and yellow on the cylinder. Take π = 3.14.

Toy rocket formed by a cone on a cylinder, with all heights and diameters labelled.
Figure 12-8 from the supplied NCERT chapter.

Solution

Board-exam working:

For the cone:

r=2.5 cm,h=6 cmr=2.5\text{ cm},\qquad h=6\text{ cm}

For the cylinder:

r′=1.5 cm,h′=26−6=20 cmr'=1.5\text{ cm},\qquad h'=26-6=20\text{ cm}

Slant height of the cone:

l=2.52+62=42.25=6.5 cml=\sqrt{2.5^2+6^2}=\sqrt{42.25}=6.5\text{ cm}

Orange area = curved area of cone + exposed ring at its base.

Ao=πrl+πr2−π(r′)2A_o=\pi rl+\pi r^2-\pi(r')^2
=3.14[(2.5)(6.5)+(2.5)2−(1.5)2]=3.14[(2.5)(6.5)+(2.5)^2-(1.5)^2]
=3.14(20.25)=63.585 cm2=3.14(20.25)=63.585\text{ cm}^2

Yellow area = curved area and bottom base of the cylinder.

Ay=2πr′h′+π(r′)2A_y=2\pi r'h'+\pi(r')^2
=3.14(1.5)[2(20)+1.5]=3.14(1.5)[2(20)+1.5]
=4.71(41.5)=195.465 cm2=4.71(41.5)=195.465\text{ cm}^2

Final answer

Ao=63.585 cm2,Ay=195.465 cm2A_o=63.585\text{ cm}^2,\qquad A_y=195.465\text{ cm}^2