The document Very 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. What is the longest pole that can be put in a room of dimensions l = 10 cm, b = 10 cm and h = 5 cm? Solution: **The longest diagonal of a cuboid =

∴ The length of the required pole (diagonal) =

**Question 2. Total surface area of a cube is 96 cm ^{2}. What is its volume? Solution:** Total surface area of the cube = 6l

∴

Thus, the volume of the cube = l^{3} = 4^{3} = 64 cm^{3 }

**Question 3. The radius of a sphere doubled. What per cent of its volume is increased? Solution:** Original volume = (4/3)πr

Increased volume = (4/3)π(2r)^{3} = 32/3πr^{3}

Increase in volume = 32/3πr^{3} - 4/3πr^{3} = 28/3πr^{3}

∴ Per cent increase in volume =

**Question 4. Write ‘True or False’ for the following statements: (i) A right circular cylinder just encloses a sphere of radius r as shown in the figure. The area of the sphere is equal to the curved surface area of the cylinder. Solution:** True.

∵ [Radius of the sphere] = [Radius of the cylinder] = r

∴ Diameter of the sphere = 2r

⇒ Height of the cylinder (h) = 2r

Now, surface area of the sphere = 4πr^{2 }

And curved surface area of the cylinder = 2πrh = 2πr (2r) = 4πr^{2}

**(ii) An edge of a cube measures ‘r’ cm. If the largest possible right circular cone is cut out of this cube, then the volume of the cone (in cm ^{3}) is 1/6**πr

∵ Height of the cone = r cm

∴ Diameter of the base of the cone = r cm

⇒ Radius of the base of the cone = (r/2) cm

Now volume of the cone

**Question 5. If the total surface area of a sphere is 154 cm ^{2}. Find its total volume. Solution:** Let ‘r’ be radius of the sphere

∴ Total S.A. = 4 π r

or

Now,

**Question 6. If the radius of a sphere is 3r then what is its volume? Solution:**

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