Sample QuestionsSurface Area And Volume of A Right Circular Cone questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The slant height of a cone is increased by $10 \%$. If the radius remains the same, the curved surface area is increased by:
- ✓
$10 \%$
- B
$12.1 \%$
- C
$20 \%$
- D
$21 \%$
Answer: A.
View full solution →The ratio of the volume of a right circular cylinder and a right circular cone of the same base and height, is:
- A
$1 : 3$
- ✓
$3 : 1$
- C
$4 : 3$
- D
$3 : 4$
Answer: B.
View full solution →If $h$, $S$ and $V$ denote respectively the height, curved surface area and volume of a right circular cone, then $3\pi\text{V}\text{h}^3-\text{S}^2\text{h}^2+\text{9V}^2$ is equal to:
- A
$8$
- ✓
$0$
- C
$4\pi$
- D
$32\pi^2$
Answer: B.
View full solution →The height of a solid cone is $12\ cm$ and the area of the circular base is $64\pi\text{cm}^2.$ A plane parallel to the base of the cone cuts through the cone $9\ cm$ above the vertex of the cone, the areas of the base of the new cone so formed is:
- A
$9\pi\text{cm}^2$
- B
$16\pi\text{cm}^2$
- C
$25\pi\text{cm}^2$
- ✓
$36\pi\text{cm}^2$
Answer: D.
View full solution →A right circular cylinder and a right circular cone have the same radius and the same volume. The ratio of the height of the cylinder to that of the cone is:
- A
$3 : 5$
- B
$2 : 5$
- C
$3 : 1$
- ✓
$1 : 3$
Answer: D.
View full solution →Statement-1 (A): A cylinder and a right circular cone have the same base and same height. If the volume of the cone is 25 cubic units, then the volume of the cylinder is 75 cubic units.
Statement-2 (R) : A cylinder and a right circular cone have the same base and same height. The volume of the cylinder is three times the volume of the cone.
- ✓
Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
- B
Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
- C
Statement-1 is True, Statement-2 is False.
- D
Statement-1 is False, Statement-2 is True.
Answer: A.
View full solution →Statement-1 (A): If the radius of right circular cone is haleved and height is doubled, the volume will be halved.
Statement-2 (R) : In a right circular cone, height, radius and slant height do not alroays be sides of a right triangle.
- A
Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
- B
Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
- ✓
Statement-1 is True, Statement-2 is False.
- D
Statement-1 is False, Statement-2 is True.
Answer: C.
View full solution →Find the length of cloth used in making a conical pandal of height 100 m and base radius 240 m, if the cloth is $100 \pi$ m wide.
View full solution →Find the area of metal sheet required in making a closed hollow cone of base radius 7 cm and height 24 cm.
Find the area of canvas required for a conical tent of height 24 m and base radius 7 m.
If the radius and slant height of a cone are in the ratio 7: 13 and its curved surface area is $286 cm^2$, find its radius.
View full solution →The height of a conical vessel is 3.5 cm. If its capacity is 3.3 litres of milk. Find the diameter of its base.
The volume of a right circular cone is $9856 \mathrm{~cm}^3$. If the diameter of the base is $28 \ cm$ , Find: Slant height of the cone.
View full solution →The volume of a right circular cone is $9856\ cm^2$. If the diameter of the base is $28\ cm$, Find: Height of the cone.
View full solution →Find the volume of the right circular cone with the following dimensions: Radius $6\ cm$, height $7\ cm.$
View full solution →Find the curved surface area of a cone, if its slant height is $60\ cm$ and the radius of its base is $21\ cm.$
View full solution →The volume of a right circular cone is 9856cm$^3$. If the diameter of the base is $28\ cm$, Find: Curved surface area of the cone.
View full solution →The diameters of two cones are equal. If their slant height are in the ratio $5 : 4$, find the ratio of their curved surfaces.
View full solution →There are two cones. The curved surface area of one is twice that of the other. The slant height of the later is twice that of the former. Find the ratio of their radii.
Find the total surface area of a cone, if its slant height is $21\ m$ and diameter of its base is $24\ m.$
View full solution →A conical pit of top diameter $3.5m$ is $12m$ deep. What is its capacity in kilolitres?
View full solution →The radius of a cone is $7\ cm$ and area of curved surface is $176cm^2.$ Find the slant height.
View full solution →Find the area of canvas required for a conical tent of height 24m and base radius $7m.$
View full solution →Monica has a piece of Canvas whose area is$ 551\ m^2$. She uses it to have a conical tent made, with a base radius of $7\ m.$ Assuming that all the stitching margins and wastage incurred while cutting amounts to approximately $1\ m^2$. Find the volume of the tent that can be made with it.
View full solution →Find the area of metal sheet required in making a closed hollow cone of base radius $7\ cm$ and height $24\ cm$.
View full solution → A bus stop is barricaded from the remaining part of the road, by using $50$ hollow cones made of recycled card board. Each cone has a base diameter of $40\ cm$ and height $1$ $m$ . If the outer side of each of the cones is to be painted and the cost of painting is $Rs$. $12$ per $m ^2$, what will be the cost of painting all these cones? (Use $\pi=3.14$ and $\sqrt{1.04}=1.02$ )
View full solution →Find the length of cloth used in making a conical pandal of height $100\ m$ and base radius $240\ m$, if the cloth is $100\pi\text{m}$ wide.
View full solution →