Premium Online Home Tutors

3 Tutor System

Starting just at 265/hour

i) radius 7 cm, slant height 25 cm

ii) height 12 cm, slant height 13 cm .

Answer :

i)Given :

Radius (r) of cone = 7 cm

Slant height (l) of cone = 25 cm

Height of cone

= \(\sqrt({l}^2 - {r}^2)\) cm

= \(\sqrt({25}^2 - {7}^2)\) cm

= \(24\) cm

We know that,

Volume of cone

= \(\frac{1}{3} {\pi} {r}^2 h\)

= \(\frac{1}{3} × \frac{22}{7} × {7}^2 × 24\) \({cm}^3\)

= 154 × 8 \({cm}^3\)

= 1232 \({cm}^3\)

Therefore, capacity of the conical vessel

= 1232 \({cm}^3\) = 1.232 litres

ii) Height (h) of cone = 12 cm

Slant height (l) of cone = 13 cm

Radius of cone

= \(\sqrt({l}^2 - {h}^2)\) cm

= \(\sqrt({13}^2 - {12}^2)\) cm

= \(5\) cm

We know that,

Volume of cone

= \(\frac{1}{3} {\pi} {r}^2 h\)

= \(\frac{1}{3} × \frac{22}{7} × {5}^2 × 12\) \({cm}^3\)

= 300 × 1.047 \({cm}^3\)

= 314.28 \({cm}^3\)

Therefore, capacity of the conical vessel = 314.28 \({cm}^3\) = 0.31428 litres

- Find the volume of the right circular cone withi) radius 6 cm, height 7 cmii) radius 3.5 cm, height 12 cm.
- The height of a cone is 15 cm. If its volume is 1570 \({cm}^3\) , find the radius of the base. (Use \({\pi}\) = 3.14)
- If the volume of a right circular cone of height 9 cm is \(48 {\pi} {cm}^3\) , find the diameter of its base.
- A conical pit of top diameter 3.5 m is 12 m deep. What is its capacity in kilolitres?
- The volume of a right circular cone is 9856 \({cm}^3\) . If the diameter of the base is 28 cm, findi) height of the coneii) slant height of the coneiii) curved surface area of the cone.
- A right triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm. Find the volume of the solid so obtained.
- If the triangle ABC in the Question 7 above is revolved about the side 5 cm, then find the volume of the solid so obtained. Find also the ratio of the volumes of the two solids obtained in Questions 7 and 8.
- A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. Find its volume. The heap is to be covered by canvas to protect it from rain. Find the area of the canvas required.

- NCERT solutions for class 9 maths chapter 1 Number Systems
- NCERT solutions for class 9 maths chapter 2 Polynomials
- NCERT solutions for class 9 maths chapter 3 Coordinate geometry
- NCERT solutions for class 9 maths chapter 4 Linear equations in two variables
- NCERT solutions for class 9 maths chapter 5 Introduction to Euclidean Geometry
- NCERT solutions for class 9 maths chapter 6 Lines and Angles
- NCERT solutions for class 9 maths chapter 7 Triangles
- NCERT solutions for class 9 maths chapter 8 Quadrilaterals
- NCERT solutions for class 9 maths chapter 9 Areas of parallelograms and triangles
- NCERT solutions for class 9 maths chapter 10 Circles
- NCERT solutions for class 9 maths chapter 11 Constructions
- NCERT solutions for class 9 maths chapter 12 Heron's Formula
- NCERT solutions for class 9 maths chapter 13 Surface areas and volumes
- NCERT solutions for class 9 maths chapter 14 Statistics
- NCERT solutions for class 9 maths chapter 15 Probability

- NCERT solutions for class 9 science chapter 1 Matter in our Surroundings
- NCERT solutions for class 9 science chapter 2 Is Matter Around Us Pure
- NCERT solutions for class 9 science chapter 3 Atoms and Molecules
- NCERT solutions for class 9 science chapter 4 Structure of the Atom
- NCERT solutions for class 9 science chapter 5 The Fundamental Unit of Life
- NCERT solutions for class 9 science chapter 6 Tissues and Fundamental unit of life
- NCERT solutions for class 9 science chapter 7 Diversity in Living Organisms
- NCERT solutions for class 9 science chapter 8 Motion
- NCERT solutions for class 9 science chapter 9 Force and Laws of Motion
- NCERT solutions for class 9 science chapter 10 Gravitation
- NCERT solutions for class 9 science chapter 11 Work and Energy
- NCERT solutions for class 9 science chapter 12 sound
- NCERT solutions for class 9 science chapter 13 Why do We Fall Ill
- NCERT solutions for class 9 science chapter 14 Natural Resources
- NCERT solutions for class 9 science chapter 15 Improvement in Food Resources