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The frustum of a regular triangular pyramid has equilateral triangle for its bases. The lower and upper base edges are $9 m$ and $3 m$ respectively. If the volume is $118.2 cu . m$ , how far apart (m) are the bases?

Important Questions on Surface Areas and Volumes

MEDIUM

Mathematics>Geometry>Surface Areas and Volumes>Frustum of a Pyramid

The radius of a sphere is reduced by

40 %

. By what percent will its volume decrease?

EASY

Mathematics>Geometry>Surface Areas and Volumes>Frustum of a Pyramid

Length of each equal side of an isosceles triangle is

10 c m

and the included angle between those two sides is

45^{°}

. Find the area of the triangle.

EASY

Mathematics>Geometry>Surface Areas and Volumes>Frustum of a Pyramid

Quantity $1$ : Area of square is $324 {cm}^{2}$ , whose perimeter is equal to perimeter of rectangle. Length of the rectangle is $4 cm$ more than breadth of the rectangle. Find the area of rectangle.

Quantity $2$ : $320 {cm}^{2}$ .

MEDIUM

Mathematics>Geometry>Surface Areas and Volumes>Frustum of a Pyramid

A sector of radius

10.5 cm

with the central angle

120^{o},

is folded to form a cone by joining the two bounding radii of the sector. What is the volume (in

{cm}^{3}

) of the cone so formed?

EASY

Mathematics>Geometry>Surface Areas and Volumes>Frustum of a Pyramid

The area of a square field is

196

sq.m. What would be the length of the rope required to fence the field from any three sides?

EASY

Mathematics>Geometry>Surface Areas and Volumes>Frustum of a Pyramid

The internal diameter of a hollow hemispherical vessel is

24

c m

. It is made of a steel sheet which is

0.5

c m

thick. What is the total surface area (in

c m^{2}

) of the vessel?

HARD

Mathematics>Geometry>Surface Areas and Volumes>Frustum of a Pyramid

The dimensions of a luggage box are

80 c m, 60 c m

and

40 c m

. How many

s q . c m

of cloth is required to cover the box?

MEDIUM

Mathematics>Geometry>Surface Areas and Volumes>Frustum of a Pyramid

If the volume of a sphere is

4851 {cm}^{3}

, then its surface area (in

{cm}^{2}

) is: (Take

π = \frac{22}{7}

)

EASY

Mathematics>Geometry>Surface Areas and Volumes>Frustum of a Pyramid

The curved surface area and the height of a right circular cylinder are

660 c m^{2}

and

10 c m

respectively. Find its diameter (in

c m

EASY

Mathematics>Geometry>Surface Areas and Volumes>Frustum of a Pyramid

Find the total surface area (in

c m^{2}

) of a right circular cylinder of diameter

21 c m

and height

10 c m

MEDIUM

Mathematics>Geometry>Surface Areas and Volumes>Frustum of a Pyramid

Calculate the surface area of the solid shown in the figure excluding the bottom surface:

Question Image

EASY

Mathematics>Geometry>Surface Areas and Volumes>Frustum of a Pyramid

x^{4} + y^{4} = 706

and

x y = 15

, find the value of

x^{2} + y^{2} + 2

HARD

Mathematics>Geometry>Surface Areas and Volumes>Frustum of a Pyramid

The circumference of the base of a conical tent is

66 m

. If the height of the tent is

36 m

, what is the area (in

m^{2}

) of the canvas used in making the tent? (Take

π = \frac{22}{7}

)

EASY

Mathematics>Geometry>Surface Areas and Volumes>Frustum of a Pyramid

What would be the area of a rectangle whose area is equal to the area of circle of radius

7 c m

EASY

Mathematics>Geometry>Surface Areas and Volumes>Frustum of a Pyramid

The length, breadth and height of a cuboidal box are in ratio

7 : 5 : 3

and its whole surface area is

27832 {cm}^{3}

. Its volume is:

MEDIUM

Mathematics>Geometry>Surface Areas and Volumes>Frustum of a Pyramid

A solid metallic cube of side

9 cm

and a solid metallic cuboid having dimensions

5 cm, 13 cm

and

31 cm

are melted to form a single cube. How much (in

₹

) is the cost to polish the new cube at a rate of

₹ 10

per

{cm}^{2}

MEDIUM

Mathematics>Geometry>Surface Areas and Volumes>Frustum of a Pyramid

The internal length, breadth and height of a cuboidal room are

12 m, 8 m

and

10 m

, respectively. The total cost (in

₹

) of the whitewashing only all four walls of the room at the cost of

₹ 25

per

m^{2}

, is _____.

EASY

Mathematics>Geometry>Surface Areas and Volumes>Frustum of a Pyramid

The radius of a sphere is doubled. The percentage of increase in its surface area is?

HARD

Mathematics>Geometry>Surface Areas and Volumes>Frustum of a Pyramid

Consider a cuboid all of whose edges are integers and whose base is square. Suppose the sum of all its edges is numerically equal to the sum of the areas of all its six faces. Then the sum of all its edges is.

MEDIUM

Mathematics>Geometry>Surface Areas and Volumes>Frustum of a Pyramid

The slant height of the frustum of a cone is

4 cm

and the perimeter of its circular bases are

18 cm

and

6 cm

respectively. Find the curved surface area of the frustum.

The frustum of a regular triangular pyramid has equilateral triangle for its bases. The lower and upper base edges are9 m and 3 m respectively. If the volume is 118.2 cu. m, how far apart (m) are the bases?

Important Questions on Surface Areas and Volumes

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The frustum of a regular triangular pyramid has equilateral triangle for its bases. The lower and upper base edges are $9 m$ and $3 m$ respectively. If the volume is $118.2 cu . m$ , how far apart (m) are the bases?