The radii of the top and bottom of a bucket are 21 cm and 14 cm . Determine the capacity and curved surface area of the bucket if its height is 24 cm .

Given: Top radius R of bucket = 21 cm , bottom radius r of the bucket = 14 cm and height h = 24 cm Volume of the frustum = 1 3 πh R 2 + r 2 + R × r = 1 3 × 22 7 × 24 21 2 + 14 2 + 21 × 14 = 22 7 × 8 441 + 196 + 294 = 22 7 × 8 × 931 = 22 × 8 × 133 = 23408 cm 3 Now curved surface area C S A of bucket is = πl R - r , Here l = h 2 + R - r 2 = 24 2 + 21 - 14 2 = 576 + 49 = 625 = 25 cm C S A = πl R - r = 22 7 25 21 - 14 = 22 7 × 25 × 7 = 550 cm 2 Hence, the volume of the bucket is 23408 cm 3 and curved surface area is 550 cm 2 .

E M B I B E

Mathematics for Class 9>Chapter 12 - Mensuration>EXERCISE 12.3>Q 17

HARD

9th Manipur Board

IMPORTANT

Earn 100

A circus tent is cylindrical upto a height of $15 m$ and conical above it. If the radius of the base is $28 m$ and the slant height of the conical part is $35 m$ , find the total area of canvas used in making the tent and the volume of air inside the tent.

Important Questions on Mensuration

HARD

9th Manipur Board

IMPORTANT

Mathematics for Class 9>Chapter 12 - Mensuration>EXERCISE 12.3>Q 18

The radii of the top and bottom of a bucket are

= {πr}^{2} (\frac{1}{3} h_{2} + h_{1})

and

14 cm

. Determine the capacity and curved surface area of the bucket if its height is

24 cm

.

HARD

9th Manipur Board

IMPORTANT

Mathematics for Class 9>Chapter 12 - Mensuration>EXERCISE 12.3>Q 19

Rain water from a horizontal roof

11 m \times 6 m

drains into a vessel in the form of a frustum of a cone. The height of the vessel is

1.4 m

and the radii of its top and bottom are

0.9 m

and

5720 m^{2}

. If the vessel is just full, find the rainfall in centimetres.

MEDIUM

9th Manipur Board

IMPORTANT

Mathematics for Class 9>Chapter 12 - Mensuration>EXERCISE 12.3>Q 20

A solid cone of height

16.8 cm

and base radius

4.2 cm

is melted and recast into a solid sphere. Determine the radius of the sphere.

MEDIUM

9th Manipur Board

IMPORTANT

Mathematics for Class 9>Chapter 12 - Mensuration>EXERCISE 12.3>Q 21

A solid sphere is melted and recast into a cone whose (base) radius is the same as that of the sphere. Show that the slant height of the cone bears a ratio