CBSE Class 10 Surface Areas and Volumes Sure Shot Questions Set 07

Question. What will be the volume of tank whose length is 10m, breadth 8m and height 6m?
Answer: \( 480m^3 \)

Question. How much aluminium sheet is required to make a box with lid of length 3m, breadth 2m and height 4m?
Answer: \( 52m^2 \)

Question. What will be the area of four walls of a room of length 12m, breadth 10m and height 9m?
Answer: \( 396m^2 \)

Question. An underground water tank is in the form of cube of side 6m. What will be its volume?
Answer: \( 216m^3 \)

Question. The volume of cube is \( 8a^3 \), find its edge.
Answer: \( 2a \)

Question. Volume of a cube is \( 1000cm^3 \). What will be the length of its edge?
Answer: \( 10cm \)

Question. The length of a diagonal of a cube is 17.32cm. Find the volume of cube. (use \( \sqrt{3} = 1.732 \))
Answer: \( 1000cm^3 \)

Question. Three cubes of the same metal, whose edges are 6, 8, 10cm are melted and formed into a single cube. Find the diagonal of the single cube.
Answer: \( 12\sqrt{3}cm \)

Question. Two cubes each of length 5m edge are joined end to end. What will be the surface area of the resulting cuboid?
Answer: \( 250m^2 \)

Question. Find the area of cardboard needed to make a rectangular box 14cm long, 9cm wide and 7cm high.
Answer: \( 574m^2 \)

Question. The total surface area of the cube is \( 216cm^2 \). Find its edge.
Answer: \( 6cm \)

Question. What will be the volume of a cylindrical tank with radius 7cm and height 2cm.?
Answer: \( 308cm^3 \)

Question. What is the number of solid spheres of radius \( \frac{1}{2}cm \), which may be formed from a solid sphere of radius 2cm?
Answer: \( 64 \)

Question. If the volume and surface area of a sphere are numerically same, then what is its radius?
Answer: \( 3 \)

Question. If height of frustum is 4cm and the radii of two bases are 3cm and 6cm respectively, find the slant height of the frustum.
Answer: \( 5cm \)

Question. Volume of right circular cylinder is \( 448 \pi cm^3 \), height of cylinder is 7cm; Find the radius.
Answer: \( 8cm \)

Question. If surface area of sphere is \( 144 \pi cm^2 \). What is its radius?
Answer: \( 6cm \)

Question. If lateral surface area of a cube is \( 64cm^2 \), what will be its edge?
Answer: \( 4cm \)

Question. Volume of hemisphere is \( 18 \pi cm^3 \), what will be its radius?
Answer: \( 3cm \)

Question. Curved surface area of a cone is \( 90 \pi cm^2 \). What will be the radius of the cone if its slant height is 90cm?
Answer: \( 1cm \)

Question. Radius of sphere is 8cm. How many small spheres of radii 4cm can be formed out of it?
Answer: \( 8 \)

Question. Volume of a cuboid is \( 240cm^3 \). If its length is 4cm, breadth is 5cm, find the height of the cuboid.
Answer: \( 12cm \)

Question. Five equal cubes, each of side 6cm, are joined end to end. Find the surface area of the resulting cuboid.
Answer: \( 792m^2 \)

Question. The area of rhombus is \( 24cm^2 \) and one of its diagonal is 8cm. What is other diagonal of the rhombus?
Answer: \( 6cm \)

Question. What is the length of the largest rod that can be put in a box of inner dimensions 30cm, 24cm and 18cm?
Answer: \( 30\sqrt{2}cm \)

Question. Curved surface area of cylinder is \( 16 \pi cm^2 \). Its radius is 4cm, then find its height.
Answer: \( 2cm \)

Question. 50 circular plates each of equal radius are placed one over the other to form a cylinder. Find the height of the cylinder so formed, thickness of each plate is 1/2cm.
Answer: \( 25cm \)

Question. There are two cones. The lateral surface area of one cone is twice the lateral surface area of second cone. The slant height of second cone is twice the slant height of first cone, find the ratio of their radii.
Answer: \( 4 : 1 \)

Question. If volume of a solid sphere is \( 288\pi cm^3 \), find its radius.
Answer: \( 6cm \)

Question. A cone of height 4cm and radius 8cm is reshaped by a child to form a sphere. Find the radius of the sphere.
Answer: \( 4cm \)

Question. A well of diameter 2m is dug 14m deep. Find the volume of the earth dug out.
Answer: \( 44m^3 \)

Question. A largest sphere is carved out of a cube of side 7cm; find the radius.
Answer: \( 3.5cm \)

Question. If the volumes of two cones are in the ratio 1 : 4 and their diameters are in the ratio 4 : 5, what would be the ratio of their heights?
Answer: \( 25 : 64 \)

Question. A right cylindrical vessel is full of water. How many right cones having the same diameter and height as those of the right cylinder will be needed to store that water?
Answer: \( 3 \)

Question. A wooden box of dimensions \( 8m \times 7m \times 6m \) is to carry rectangular boxes of dimension \( 8cm \times 7cm \times 6cm \), find the maximum number of boxes that can be carried out in the wooden box.
Answer: \( 10,00,000 \)

Question. Find the slant height of a cone, if height 12cm and radius is 5cm.
Answer: \( 13cm \)

Question. If the semi-vertical angle of a cone of height 3cm is \( 60^\circ \), find its volume.
Answer: \( 27 \pi cm^3 \)

Question. Find the edge of cube if volume of the cube is equal to the volume of cuboid of dimensions \( 8 \times 4 \times 2 \).
Answer: \( 4cm \)

Question. The volume of a 8cm x 4cm x 2cm cylindrical rod is \( 980 \pi cm^3 \). If its height is 20cm, find the radius of its cross section.
Answer: \( 7cm \)

Question. Find the volume of cone of height 2h and radius r.
Answer: \( \frac{2}{3} \pi r^2 h \)

Question. A right circular cylinder is closed at both ends, whose flat area is equal to its total curve surface. What is the relationship between r and h?
Answer: \( r = h \)

Question. Find the radius of the largest right circular cone that can be cut out of a cube whose edge is 9cm.
Answer: \( 4.5cm \)

Question. The volume of a room is \( 5760m^3 \). Its length and width are 24m and 20m, find the height.
Answer: \( 12m \)

Question. The Circumference of the circular edge of solid hemispherical ball is 132cm. Find the radius of ball.
Answer: \( 21cm \)

Question. 500 persons took dip in a rectangular tank which is 80m long and 50m broad. What is the rise in level of water in the tank if the average displacement of water by a person is \( 0.04m^3 \)?
Answer: \( 0.5cm \) or \( .005m \)

Question. If the radius and height of a cylinder are in the ratio 2 : 7 and its volume is \( 88m^3 \), then what will be its radius?
Answer: \( 2m \)

Question. If a sphere of diameter 12cm is melted and drawn into a wire of diameter 0.2cm, find the length of the wire.
Answer: \( 288m \)

Question. What is the total surface area of a solid hemisphere of radius R?
Answer: \( 3 \pi R^2 \)

Question. Cube of sides 2cm is cut down into cubes of sides 1cm. What is the ratio of surface area of smaller cubes to that of larger cube?
Answer: \( 1 : 4 \)

Question. In a shower, there is 5cm rain falls. Find in cubic metre the volume of water that falls on 2 hectares of ground. (\( 1 \text{ hectare} = 10,000 m^2 \))
Answer: \( 1000m^3 \)