**Chapter 9 Surface Area and Volume Practice Set 9.1**

Chapter 9 Surface Area and Volume Practice Set 9.1

**Question 1.Length, breadth and height of a cuboid shape box of medicine is 20 cm, 12 cm and 10 cm respectively. Find the surface area of vertical faces and total surface area of this box.Given: For cuboid shape box of medicine,length (l) = 20 cm, breadth (b) = 12 cm and height (h) = 10 cm.To find: Surface area of vertical faces and total surface area of the boxSolution:**

i. Surface area of vertical faces of the box

= 2(l + b) x h

= 2(20+ 12) x 10

= 2 x 32 x 10

= 640 sq.cm.

ii. Total surface area of the box

= 2 (lb + bh + lh)

= 2(20 x 12+ 12 x 10 + 20 x 10)

= 2(240 + 120 + 200)

= 2 x 560

= 1120 sq.cm.

∴ The surface area of vertical faces and total surface area of the box are 640 sq.cm, and 1120 sq.cm, respectively.

**Question 2.Total surface area of a box of cuboid shape is 500 sq.unit. Its breadth and height is 6 unit and 5 unit respectively. What is the length of that box?Given: For cuboid shape box,breadth (b) = 6 unit, height (h) = 5 unit Total surface area = 500 sq. unit.To find: Length of the box (l)Solution:**

**Question 3.Side of a cube is 4.5 cm. Find the surface area of all vertical faces and total surface area of the cube.Given: Side of cube (l) = 4.5 cmTo find: Surface area of all vertical faces and the total surface area of the cubeSolution:**

i. Area of vertical faces of cube = 4l

^{2}

= 4 (4.5)

^{2}= 4 x 20.25 = 81 sq.cm.

ii. Total surface area of the cube = 6l

^{2}

= 6 (4.5)

^{2}

= 6 x 20.25

= 121.5 sq.cm.

∴ The surface area of all vertical faces and the total surface area of the cube are 81 sq.cm, and 121.5 sq.cm, respectively.

**Question 4.Total surface area of a cube is 5400 sq. cm. Find the surface area of all vertical faces of the cube.Given: Total surface area of cube = 5400 sq.cm.To find: Surface area of all vertical faces of the cubeSolution:**

i. Total surface area of cube = 6l

^{2}

∴ 5400 = 6l

^{2}

∴ l

^{2}= 900

ii. Area of vertical faces of cube = 4l

^{2}

= 4 x 900 = 3600 sq.cm.

∴ The surface area of all vertical faces of the cube is 3600 sq.cm.

**Question 5.Volume of a cuboid is 34.50 cubic metre. Breadth and height of the cuboid is 1.5 m and 1.15 m respectively. Find its length.Given: Breadth (b) = 1.5 m, height (h) = 1.15 mVolume of cuboid = 34.50 cubic metreTo find: Length of the cuboid (l)Solution:**

Volume of cuboid = l x b x h

∴ 34.50 = l x b x h

∴ 34.50 = l x 1.5 x 1.15

= 20

∴ The length of the cuboid is 20 m.

**Question 6.What will be the volume of a cube having length of edge 7.5 cm ?Given: Length of edge of cube (l) = 7.5 cmTo find: Volume of a cubeSolution:**

Volume of a cube = l

^{2}

= (7.5)

^{3}

= 421.875 ≈ 421.88 cubic cm

∴The volume of the cube is 421.88 cubic cm.

**Question 7.Radius of base of a cylinder is 20 cm and its height is 13 cm, find its curved surface area and total surface area, (π = 3.14)Given: Radius (r) = 20 cm, height (h) = 13 cmTo find: Curved surface area andthe total surface area of the cylinderSolution:**

i. Curved surface area of cylinder = 2πrh

= 2 x 3.14 x 20 x 13

= 1632.8 sq.cm

ii. Total surface area of cylinder = 2πr(r + h)

= 2 x 3.14 x 20(20 + 13)

= 2 x 3.14 x 20 x 33 = 4144.8 sq.cm

∴ The curved surface area and the total surface area of the cylinder are 1632.8 sq.cm and 4144.8 sq.cm respectively.

**Question 8.Curved surface area of a cylinder is 1980 cm ^{2} and radius of its base is 15 cm. Find the height of the cylinder. (π =22/7)Given: Curved surface area of cylinder = 1980 sq.cm., radius (r) = 15 cmTo find: Height of the cylinder (h)Solution:**

Curved surface area of cylinder = 2πrh

∴ h = 21 cm

∴ The height of the cylinder is 21 cm.