Similar Solids Worksheet

**Page 2**

11.

Which of the following is / are correct?

1. Similar solids have same shape.

2. The ratio of surface areas of similar solids is the same as the ratio of its volumes.

3. The ratio of volumes of two similar solids is thrice the ratio any of its corresponding sides.

4. Similar solids have same volume.

1. Similar solids have same shape.

2. The ratio of surface areas of similar solids is the same as the ratio of its volumes.

3. The ratio of volumes of two similar solids is thrice the ratio any of its corresponding sides.

4. Similar solids have same volume.

a. | (1) and (2) only | ||

b. | (1) and (4) only | ||

c. | (1) only | ||

d. | (1) and (3) only |

So similar solids do not possess the same dimensions.

Ratio of surface areas of similar solids is the square of the similarity ratio.

Ratio of volumes of similar solids is the cube of its similarity ratio.

So, statement (1) only is correct.

Correct answer : (3)

12.

A wooden paperweight in the shape of a cone weighs 0.12 lb. What is the weight of a similar paperweight, which has double the dimensions of the first one?

a. | 0.96 lb | ||

b. | 0.6 lb | ||

c. | 0.5 lb | ||

d. | 2 lb |

So, the ratio of the volume is 1

[Let

[Cross-product property.]

The larger paperweight weighs 0.96 lb.

Correct answer : (1)

13.

A rectangular matchbox contains 45 sticks. If a jumbo box is made by doubling all the dimensions of this rectangular matchbox, then how many sticks can the jumbo box hold?

a. | 180 | ||

b. | 2025 | ||

c. | 90 | ||

d. | 360 |

So, the ratio of the volumes is 1

[Let the number of sticks in the jumbo box be

[Cross - product property.]

The number of sticks that jumbo matchbox can hold = 360.

Correct answer : (4)

14.

The similarity ratio and the ratio of volumes of two similar solids are $x$ : 2 and 8 : $x$ . Find the ratio of their surface areas.

a. | 2 : 1 | ||

b. | 4 : 1 | ||

c. | 8 : 1 | ||

d. | 16 : 1 |

Ratio of volumes of the two solids =

[Definition.]

[Cross - product property.]

[Find fourth root of each side.]

So, similarity ratio =

[Substitute 4 for

So, the ratio of the surface areas of the two solids = (2)

[Definition of ratio of surface areas.]

Correct answer : (2)

15.

Which of the following is correct?

a. | B | ||

b. | A | ||

c. | D | ||

d. | C |

[Similarity ratio is

[Substitute

So, ratio of the surface areas is

[Substitute

So, ratio of the volumes is

[Substitute

Correct answer : (2)

16.

The cones shown in the figure are similar. Find the value of $l$ if $a$ = 6 units , $b$ = 9 units and $x$ = 8 units .

a. | 17 units | ||

b. | 15 units | ||

c. | 12 units | ||

d. | 14 units |

[Cross - product property.]

Correct answer : (3)

17.

The cones shown in the figure are similar. Find the area of the base of smaller cone if $l$ = 6 units, $x$ = 10 units, and $y$ = 12 units .

a. | 400$\pi $ units ^{2} | ||

b. | 100$\pi $ units ^{2} | ||

c. | 25$\pi $ units ^{2} | ||

d. | 5$\pi $ units ^{2} |

The area of the base of the smaller cone =

=

[Substitute 3 for

Correct answer : (3)

18.

The cylinders shown are similar. Find the volume of the larger cylinder if $x$ = 8 units , $a$ = 12 units and $b$ = 15 units .

a. | 1500 $\pi $ units ^{3} | ||

b. | 768 $\pi $ units ^{3} | ||

c. | 960 $\pi $ units ^{3} | ||

d. | 300 $\pi $ units ^{3} |

The volume of the larger cylinder =

[Formula.]

=

[Substitute 10 for

Correct answer : (1)

19.

The rectangular boxes shown are similar. The volume of the larger box is _______ .

[Given$a$ = 3 units , $b$ = 4 units , $c$ = 5 units and $x$ = 9 units .]

[Given

a. | 15 cubic units | ||

b. | 1620 cubic units | ||

c. | 3240 cubic units | ||

d. | 810 cubic units |

[Cross - product property.]

The volume of the larger box =

= 9 × 12 × 15 = 1620 cubic units

[Substitute 12 for

Correct answer : (2)

20.

The similarity ratio, ratio of surface areas and of volumes of two similar solids are in

a. | no specific relation | ||

b. | arithmetic progression | ||

c. | harmonic progression | ||

d. | geometric progression |

So, the ratio of their surface areas =

[Definition.]

Clearly

Correct answer : (4)