Surface Area An...

A metallic right circular cone of height 18 cm and base radius 7 cm is melted into a cuboid whose two sides measure 11 cm and 6 cm. What is the length of the third side of the cuboid?

A cylinder of length 14 cm and radius 4 cm is cut out of a cube of side 12 cm.

How many small cuboids of length, breadth and height of 4 cm, 4 cm and 2 cm, respectively, can be obtained from the remaining solid?

The dimensions of a plot of land are 20 m by 9 m. A pit 10 m long, 4.5 m wide and 3 m deep is dug in one corner of the plot and the earth removed is spread evenly over the remaining area. What is the rise in the height of this area as a result of this operation?

A toy is in the shape of a cone surmounted on a hemisphere of same radius. If s, p and q, respectively is the total surface area of the toy, the curved surface area of the hemisphere and the curved surface area of the cone, then which of the following relationships is true?

A metallic cylinder with 70 cm height and base diameter 15 cm is surmounted by a hemisphere of same diameter. Find the mass of the solid; given that 1 cm³ of metal has 10 g of mass (approximately). (Take = )

A construction company wants to partition a hall in its office into two equal parts, so it makes a wall in the centre of the hall. The length and breadth of the wall are 12 m and 7.5 cm, respectively. The number of cement blocks required to construct the wall is 1600 and the dimensions of each cement block are 25 cm x 15 cm x 12 cm. Find the height of the wall (in metres).

Three solid metallic spheres of radii 6, 8 and 10 centimetres are melted to form a single solid sphere. The radius of the sphere so formed is

Some spherical balls are made from scrap paper. The thickness of a spherical ball is 4 cm, where the outer radius is 1.5 times the inner radius. What will be the approximate volume of the scrap paper used?

A toy is prepared using a hemisphere which is surmounted by a cone. The diameter of the hemisphere is d and the radius of the cone is half of the diameter of the hemisphere. The height of the toy is twice the height of the hemisphere. According to this information, which of the following expressions represents the volume of the toy?(Write the answer in cubic units)

The ratio of the base radii of two right circular cones is 7 : 4 and the slant height of these right circular cones is same. Which of the following represents the ratio of their curved surface areas?

The volume of a cone increases by x cubic units after its radius is increased by 6 units. Increasing the height of the same cone by 9 units also increases the volume by x cubic units. If the original height is 3 units, then the original radius is

A cylinder of the maximum possible size is made out of a solid wooden cube with each side 20 cm. What percentage of material (approx.) is left in this process?(Take π = 3.14)

What will be the area of a given cricket ground if a ground level machine in a cylindrical shape, having a radius of 49 cm and length 160 cm, needs 600 revolutions to complete its levelling?

Cost of electroplating a spherical steel ball is Rs. 887.04. If 9 paise are charged per square cm, then what is the diameter of the spherical steel ball? (π = 22/7)

Raman while making a lamp post in spherical shape decides to reduce the diameter of the lamp post by a quarter. What effect will it have on curved surface area of the lamp post?

Mariya is an artist and is very precise about her inventory to be used in assignments. She undertakes the work of colouring the bricks, which are to be used for building a wall. She decides to use a bucket of paint which has sufficient paint to colour 8.9 square metre of area. How many bricks of dimensions 55 cm, 20 cm and 15 cm will she paint regardless the total bricks available, if she decides to use only the fixed amount of paint available with her?

Anju has used cloth on edges of a rectangular aquarium to make it look fancy. The length of the aquarium is 60 cm, whereas the width and height are 50 cm each.

(i) What is the total surface area of the aquarium?
(ii) How much length of cloth is used on all edges?

The decorative block shown in the figure is made up of two solids, a cube and a hemisphere. The base of the block is a cube with edge 5 cm and the hemisphere fixed on the top has a diameter of 4.2 cm. The total surface area of the block is

In a stable, Ram prepares liquid diet for each horse in a cylinder shaped bowl of diameter 14 cm, filled up to a height of 8 cm. What quantity of liquid diet must be prepared to satisfy 500 horses?

The curved surface areas of a right-circular cone and a hemisphere, having the same radius are in the ratio of . Find the ratio of the height of the cone to the radius of the hemisphere.

Match the following.

A sphere of diameter 21 cm is placed on a cuboid of dimensions 33 cm, 21 cm, and 49 cm. Both are melted to form a large sphere. Find the ratio of the radius of small sphere to the radius of large sphere. {Take pi = 22/7}

Directions: Read the given statements and write 'T' for true and 'F' for false.

(i) If the radius of a hemisphere and a cylinder is same, then volume of the hemisphere : volume of the cylinder = 3 (radius of the hemisphere or the cylinder) : 2 (height of the cylinder).
(ii) In a cylinder having equal radius and height, if both radius and height are doubled, the total surface area would become 9 times.
(iii) If the radius of a cylinder and a cone is same, and the height of the cylinder is equal to the slant height of the cone, then the ratio of the curved surface area of the cylinder to that of the cone is 2 : 1.

The volume of a cylinder is 5184 cm³. A cone of radius and height same as those of cylinder is carved out of it. The cone is then melted to form a cube and then cut into two equal cuboids. Both the small cuboids are then plated gold at the cost of Rs. 2.50 per cm². Find the total cost of gold plating.

Which of the following statements is CORRECT?

(i) The radius of the base of a cone is equal to its height. If the height of the cone is decreased by one-quarter without changing the radius, then the new slant height istimes its previous slant height.
(ii) If the radius of a hemisphere is double of the radius of a sphere, their volumes would be same.