The diagonal of a cube is 16 36 cm . Find it's surface area and volume.

Given, diagonal of cube, d = 16 3 cm We know that, diagonal of a cube = 3 a cm , where a is the length of side. Now, 3 a = 16 3 ⇒ a = 16 cm Surface area of cube = 6 a 2 = 6 × 16 2 = 1536 cm 2 a = 16 cm Volume of cube = a 3 = 16 3 = 4096 cm 3 Therefore, surface area of cube is 1536 cm 2 and volume of the cube is 4096 cm 3

E M B I B E

Mathematics>Chapter 14 - Mensuration>TEST YOUR SKILLS>Q 4

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8th CBSE

IMPORTANT

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Two cubes of volume $512 {cm}^{3}$ each are joined end to end. The surface area of the resulting cuboid is $k {cm}^{2}$ . Then find the value of $k$ .

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Important Questions on Mensuration

HARD

8th CBSE

IMPORTANT

Mathematics>Chapter 14 - Mensuration>TEST YOUR SKILLS>Q 1

The parallel sides

AB

and

DC

of a trapezium

ABCD

are

51 cm

and

30 cm

respectively. If the other sides

AD

and

BC

are

20 cm

and

13 cm

respectively. Find the distance between the parallel sides and the area of the trapezium.

MEDIUM

8th CBSE

IMPORTANT

Mathematics>Chapter 14 - Mensuration>TEST YOUR SKILLS>Q 2

The area of a trapezium is

540 {cm}^{2}

If the ratio of parallel sides is

7 : 5

distance between then is

18 cm

, find the lengths of parallel sides.

MEDIUM

8th CBSE

IMPORTANT

Mathematics>Chapter 14 - Mensuration>TEST YOUR SKILLS>Q 5

The area of three adjacent faces of a cuboid are

x, y

and

z

units. If the volume is

V

cubic units, then prove that

V^{2} = x y z

MEDIUM

8th CBSE

IMPORTANT

Mathematics>Chapter 14 - Mensuration>TEST YOUR SKILLS>Q 6

The diagonal of a cube is

16 \sqrt{36} cm

. Find it's surface area and volume.

MEDIUM

8th CBSE

IMPORTANT

Mathematics>Chapter 14 - Mensuration>TEST YOUR SKILLS>Q 7

A well with

10 m

inside diameter is dug

8.4 m

deep. Earth taken out of it is spread all around it to a width of

7.5 m

to form an embankment. Find the height of embankment.

HARD

8th CBSE

IMPORTANT

Mathematics>Chapter 14 - Mensuration>TEST YOUR SKILLS>Q 8

The total surface area of a cylinder is

462 {cm}^{2}

. If it's curved surface area is one third of its total surface area, then the volume of the cylinder is

k {cm}^{3}

. Find the value of

k

.

MEDIUM

8th CBSE

IMPORTANT

Mathematics>Chapter 14 - Mensuration>TEST YOUR SKILLS>Q 9

Top surface of a raised platform is in the shape of regular octagon as shown in the figure, if the area of the octagonal figure is $k m^{2}$ , find the value of $k$ .

EASY

8th CBSE

IMPORTANT

Mathematics>Chapter 14 - Mensuration>Multiple Choice Questions>Q 1

The volume of a cube whose edge is