Find the surface area and the volume of a cuboid of dimensions 5 m × 4 m × 3 m . Also, find the length of a diagonal.

We know that the total surface area, volume and the diagonal of a cuboid are given by 2 l b + b h + h l , l b h and l 2 + b 2 + h 2 , respectively, where l = the length, b = the breadth and h = the height of the cuboid. Given that the cuboid has the dimensions 5 m × 4 m × 3 m . So, here, l = 5 m , b = 4 m and h = 3 m . Thus, the total surface area of the cuboid = 2 5 × 4 + 4 × 3 + 3 × 5 = 2 20 + 12 + 15 = 2 × 47 = 94 m 2 . The volume of the cuboid = 5 × 4 × 3 = 60 m 3 . And, the diagonal of the cuboid = 5 2 + 4 2 + 3 2 = 25 + 16 + 9 = 50 = 5 2 m . Therefore, the surface area, the volume and the length of a diagonal of the cuboid are 94 m 2 , 60 m 3 and 5 2 m , respectively.

E M B I B E

CBSE Syllabus Standard Mathematics for Class IX>Chapter 13 - Surface Areas and Volumes>Multiple Choice Questions>Q 18

EASY

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If the radius of a sphere is $2 r$ , then its volume will be

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Important Questions on Surface Areas and Volumes

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IMPORTANT

CBSE Syllabus Standard Mathematics for Class IX>Chapter 13 - Surface Areas and Volumes>Multiple Choice Questions>Q 19

If the diameter of a sphere is

16 cm

, then its surface area is

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CBSE Syllabus Standard Mathematics for Class IX>Chapter 13 - Surface Areas and Volumes>Multiple Choice Questions>Q 20

If the radius of a hemisphere is

5 cm

, then its volume is

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CBSE Syllabus Standard Mathematics for Class IX>Chapter 13 - Surface Areas and Volumes>Multiple Choice Questions>Q 21

If the ratio of the diameters of the two spheres is

3 : 5

, then the ratio of their surface areas is

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CBSE Syllabus Standard Mathematics for Class IX>Chapter 13 - Surface Areas and Volumes>Multiple Choice Questions>Q 22

The radius of a hemispherical balloon increases from

6 cm

to

12 cm

as air is being pumped into it. The ratio of the surface areas of the balloon in the two cases is

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CBSE Syllabus Standard Mathematics for Class IX>Chapter 13 - Surface Areas and Volumes>Higher Order Thinking Skills (HOTS)>Q 1

The figure below shows a victory stand, each face is rectangular. All measurements are in centimetres. Find its volume and surface area (the bottom of the stand is open).

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