Surface Area And Volume Of Solid Shape – Mensuration

EXAMPLE

The base radius and height of a right circular cone is 7 cm and 24 cm. Find its curved surface area, total surface area and volume.

SOLUTION:

r = 7 cm and h = 24 cm. So, slant height l = 22

Curved surface area = πrl = 7 /22 × 7 X 24 cm2 = 550 cm²

Total surface area = πrl + πr² = (550 + 7/ 22 × 49) cm2 = (550 + 154) cm2 = 704 cm²

Volume =  1/3 πr² h =  1/3 ×  22/7 × 49 × 24 cm3 = 1232 cm³

 EXAMPLE

A conical tent is 6 m high and its base radius is 8 m. Find the cost of the canvas required to make the tent at the rate of ` 120 per m2 (Use π = 3.14)

Solution:

Let the slant height of the tent be x metres.

By Pythagoras theorem,

X² =6² +8²

X² = 6²+8²

X = √(6²+8) = √100

X = 10m.

Thus, slant height of the tent is 10 m.

Curved surface area = πrl   = 3.14 × 8 × 10 cm2 = 251.2 m²

The material required = 251.2 x 120 = 30144m²

The measure of the space region enclosed by a solid figure is called its volume.

MENSURATION SURFACE AREAS AND VOLUMES OF SOLID FIGURES

Practice questions (Use the form below to submit answer for discussion)

(i) Surface area of cylinder open at one end = ______, where r and h are the radius and height of the cylinder.

(ii)Volume of the cylinder of radius r and height h = __________

(iii) Curved surface area of cone = ____________, where r and l are respectively the ______ and _________ of the cone.

(iv) Surface area of a sphere of radius r = __________

(v) Volume of a hemisphere of radius r = ___________ 2. Choose the correct answer from the given four options:

(vi)The edge of a cube whose volume is equal to the volume of a cuboid of dimensions 63 cm × 56 cm × 21 cm is

(A) 21 cm (B) 28 cm (C) 36 cm (D) 42 cm

(vii) If radius of a sphere is doubled, then its volume will become how many times of the original volume?  (A) 2 times (B) 3 times (C) 4 times (D) 8 times

(viii) Volume of a cylinder of the same base radius and the same height as that of a cone is

(A) the same as that of the cone (B) 2 times the volume of the cone (C) 3 1 times the volume of the cone (D) 3 times the volume of the cone.

(ix) If the surface area of a cube is 96 cm2 , then find its volume

(x) Find the surface are a and volume of a cuboid of length 3m, breadth 2.5m and height 1.5 m.

(xi) Find the surface area and volume of a cube of edge 1.6 cm.

(xii) Find the length of the diagonal of a cuboid of dimensions 6 cm × 8 cm × 10 cm.

(xiii) Find the length of the diagonal of a cube of edge 8 cm.

(xiv) Find the total surface area of a hollow cylindrical pipe open at the ends if its height is 10 cm, external diameter 10 cm and thickness 12 cm (use π = 3.14).

(xv) (i) Find the slant height of a cone whose volume is 12936 cm3 and radius of the base is 21 cm.(ii) find its total surface area.

(xvi) A well of radius 5.6 m and depth 20 m is dug in a rectangular field of dimensions 150m×70m and the earth dug out from it is evenly spread on the remaining part of the field. Find the height by which the field is raised.

(xvii) Find the radius and surface area of a sphere whose volume is 606.375 m³