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The maximum length of a pencil that can be kept in a rectangular box of dimensions 8 cm x 6cm x 2 cm, is

A) \( \Large 2\sqrt{13} cm \)
B) \( \Large 2\sqrt{14} cm \)
C) \( \Large 2\sqrt{26} cm \)
D) \( \Large 10\sqrt{2} cm \)

Correct Answer:



C) \( \Large 2\sqrt{26} cm \)

Description for Correct answer:

Length of largest pencil that can be kept in a box

= Diagonal of box = \( \Large \sqrt{l^{2}+b^{2}+h^{2}} \)

where, l = 8 cm, b = 6 cm, h = 2 cm

= \( \Large \sqrt{64 + 36 + 4} \)

= \( \Large \sqrt{104} = 2\sqrt{26 cm} \)

Part of solved Volume and surface area questions and answers : >> Elementary Mathematics >> Volume and surface area

Comments

Similar Questions

1). Internal length, breadth and height of a rectangular box are 10 cm, 8 cm and 6 cm, respectively. How many boxes are needed which can be packed in a cube whose volume is 6240 cu. cm.?

A). 12

B). 13

C). 15

D). 17

2). A cube has each edge 2 cm and a cuboid is 1 cm long, 2 cm wide and 3 cm high. The paint in a certain container is sufficient to paint an area equal to 54 \( \Large cm^{2} \). Which one of the following is correct?

A). Both cube and cuboid can be painted

B). Only cube can be painted

C). Only cuboid can be painted

D). Neither cube nor cuboid can be painted

3). The whole surface area of a rectangular block is 8788 sq cm. If length, breadth and height are in the ratio of 4 : 3 : 2, then find the length.

A). 26 cm

B). 52 cm

C). 104 cm

D). 13 cm

4). What are the dimensions (length, breadth and height, respectively) of a cuboid with volume 720 cu cm, surface area 484 sq cm and the area of the base 72 sq cm?

A). 9, 8 and 10 cm

B). 12, 6 and 10 cm

C). 18, 4 and 10 cm

D). 30, 2 and 12 cm

5). The volume of a cube is equal to sum of its edges. What is the total surface area in square units?

A). 12

B). 36

C). 72

D). 144

6). If each side of a cube is decreased by 19%, then decrease in surface area is

A). 40%

B). 38.40%

C). 35%

D). 34.39%

7). The diameter of the base of a right circular cylinder is 14 cm, while its length is 40 cm. Find the total surface area of the cylinder.

A). 2068 sq cm

B). 1825 sq cm

C). 1925 sq crn

D). 2160 sq cm

8). If the lateral surface area of a cylinder is 94.2 sq cm and its height is 5 cm, then find the radius of its base. (n = 3.14)

A). 5 cm

B). 8 cm

C). 3 cm

D). 4cm

9). A rod of 2 cm diameter and 30 cm length is converted into a wire of 3 in length of uniform thickness. The diameter of the wire is

A). \( \Large \frac{2}{10} \) cm

B). \( \Large \frac{2}{\sqrt{10}} \) cm

C). \( \Large \frac{1}{\sqrt{10}} \) cm

D). \( \Large \frac{1}{10} \) cm

10). What is the height of a solid cylinder of radius 5 cm and total surface area is 660 sq cm?

A). 10 cm

B). 12 cm

C). 15 cm

D). 16 cm