The document Short Answers Type Questions- Surface Areas and Volumes Class 9 Notes | EduRev is a part of the Class 9 Course Mathematics (Maths) Class 9.

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**Question 1. The length, breadth and height of a room are 4 m, 3 m and 3 m respectively. Find the lateral surface area of the room. Solution:** Here, l = 4 m, b = 3 m and h = 3 m.

Lateral surface area = Area of four walls = 2(l + b)h = 2(4 + 3) x 3 m

âˆ´ The required lateral surface of the room is 42 m

**Question 2. The floor area of a room is 100 m ^{2} and its height is 8 m. Find its volume. Solution:** âˆµ Volume of a cuboid = [Base area] x Height

âˆ´ Volume of the room = [Area of the floor] x height = 100 m

Thus, the volume of the room = 800 m

**Question 3. If the total surface area of a cube is 216 cm ^{2}, then find its volume. Solution: **Let each side of the cube be x.

âˆ´ Total surface area = 6x2

â‡’ 6x

â‡’ x

â‡’ x = âˆš36 = 6 cm

âˆ´ Volume = (side)^{3} = 6^{3} = 6 x 6 x 6

= 216 cm^{3}

**Question 4. If the circumference of the base of a right circular cylinder is 110 cm, then find its base area. Solution: **Let r be the radius of the base of the cylinder.

âˆ´ Circumference = 2Ï€r = 2 x(22/7)x r

Now, 2 x(22/7) x r= 110

â‡’

Now, Base area =

**Question 5. The curved surface area of a cylinder is 4400 cm ^{2}. If the circumference of its base is 110 cm, then find its height. Solution: **Curved surface area of the cylinder = 2Ï€rh

Circumference = 2Ï€r

âˆ´

Thus, the height of the cylinder is 40 cm.

**Question 6. The radii of two cylinders are in the ratio of 2 : 3 and heights are in the ratio of 5 : 3. Find the ratio of their volumes. Solution: **Ratio of the radii = 2 : 3 Let the radii be 2r and 3r Also, their heights are in the ratio of 5:3 Let the height be 5h and 3h

âˆ´ Ratio of their volumes =

**Question 7. If the radius of a sphere is doubled, then find the ratio of their volumes. Solution:** Let the radius of the original sphere = r

âˆ´ Radius of new sphere = 2r

âˆ´ Ratio of their volumes =

**Question 8. If the radius of a sphere is such that Ï€r ^{2} = 6cm^{2} then find its total surface area.**âˆµ Ï€r

Solution:

âˆ´ Curved S.A. of the hemisphere

= 2 Ã— 6 cm

Also, plane S.A. of the hemisphere = Ï€ r

â‡’ Total S.A. = C.S.A. + plane S.A. = 12 cm

**Question 1. The surface area of a sphere of radius 5 cm is five times the area of the curved surface of a cone of radius 4 cm. Find the height and the volume of the cone (taking Ï€ = **(22/7)**. Solution:** Surface area of the sphere = 4Ï€r

Curved surface area of the cone (with slant height as â€˜â„“â€™) = Ï€râ„“ = Ï€ Ã— 4 Ã— â„“ cm

Since,

âˆ´ 4 Ã— Ï€ Ã— 5 Ã— 5 = 5 Ã— Ï€ Ã— 4 Ã— â„“

â‡’

âˆ´ Volume of the cone =

**Question 2. The radius of a sphere is increased by 10%. Ï€rove that the volume will be increased by 33.1% apÏ€roximately. Solution: **The volume of a sphere =

Increased radius =

âˆ´ Increased volume =

= (4/3) x Ï€ x 1.331r^{3}

Thus, Increase in volume

âˆ´ Percentage increase in volume

= 0.331 Ã— 100%

= 33.1%.

**Question 3. Find the slant height of a cone whose radius is 7 cm and height is 24 cm. Solution:** Here, h = 24 cm and r = 7 cm

Since,

= 25 cm

âˆ´ Slant height = 25 cm.

**Question 4. The radius of a cylinder is 7 cm. If its volume is 2002 cm ^{3}, then find its height and total surface area. Solution: **Here, radius (r) = 7 cm

âˆ´ Volume of the cylinder = = Ï€r

Now,(22/7)x 7 x 7 x h = 2002

âˆ´

Now, total surface area of the cylinder = 2Ï€r^{2} + 2Ï€rh = 2Ï€r(r + h)

= 2 x(22/7) x 7 x (7 + 13) cm^{2 }

= 44 Ã— 20 cm^{2} = 880 cm^{2 }

**Question 5. The diameter of a road roller, 120 cm long is 84 cm. If it takes 500 complete revolutions to level a playground, find the cost of levelling it at ****2 per square metre. Solution:** Here, radius (r) = 42 cm

Length of the roller = Height of the cylinder

â‡’ h = 120 cm

âˆ´ Curved surface area of the roller = 2Ï€rh =2 x(22/7) x 42 x 120 cm

= 2 x 22 x 6 x 120 cm

âˆ´ Area levelled in one revolution = 31680 cm

â‡’ Area levelled in 500 revolutions = 31680 x 500 cm^{2}

âˆ´ Cost of levelling the playground = 2 x 15840 = 31680.

**Question 6. A conical tent of radius 7 m and height 24 m is to be made. Find the cost of the 5 m wide cloth required at the rate of ****50 per metre. Solution:** Radius of the base of the tent (r) = 7 m

Height (h) = 24 m

Slant height (â„“)=

Now, curved surface area of the conical tent = Ï€râ„“

= (22/7) x 7 x 25 m^{2} = 22 x 25 m^{2} = 550 m^{2 }

Let â€˜â„“â€™ be the length of the cloth.

âˆ´ â„“ x b = 550

â‡’ â„“ x 5 = 550

â‡’ â„“ = (550/5) m = 110 m

âˆ´ Cost of the cloth = 50 x 110 = 5500.

**Question 7. How many lead balls, each of radius 1 cm, can be made from a sphere of radius 8 cm? Solution:** Radius of the lead ball (r) = 1 cm

âˆ´ Volume of a lead ball = x 1 x 1 x 1 cm^{3}

= (4/3) x (22/7) cm^{3}

Radius of the sphere (r) = 8 cm

âˆ´ Volume of a sphere = x 8 x 8 x 8 cm^{3}

Let the required number of balls = n

âˆ´ [Volume of n-lead balls] = [Volume of the sphere]

Thus, the required number of balls is 512.

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