#### The lateral surface area of a cuboid, whose length, breadth and height are 12 cm, 8 cm, and 4.5 cm, respectively, is ____.

#### If the volume of a cube is 729 cm^{3}, then its total surface area is ____.

Let the length of the edge of the cube be l cm. Given, the volume of cube = 729 cm^{3} ⇒ l^{3} = 729 ⇒ l = 9 We know that, Total surface area of the cube = 6 l^{2} = 6 × 81 = 486 cm^{2} Hence, the total surface area of cube is 486 cm^{2}

#### If the difference between the total surface area and the lateral surface area of a cube is 50 m^{2}, then the length of edge of the cube is ____.

Let a be the length of edge of the cube. Lateral surface area of a cube = 4 a^{2} Given, 6 a^{2} - 4 a^{2}= 50 m^{2} ⇒ 2 a^{2} = 50 ⇒ a^{2} = 25 ⇒ a = 5 m Hence, the length of edge of the cube is 5 m.

#### If the radius and height of a cylinder are 10cm, 14cm respectively, then its lateral surface area is ____.

Given, height of the cylinder, h = 14 cm, Radius of the cylinder, r = 10 cm Lateral surface area of the cylinder = 2 πrh = 2 × 22 /7 × 10 × 14 = 880 cm^{2} Hence, the lateral surface area of the cylinder is 880 cm^{2}

#### If the radius and height of a cylinder are r and h respectively, then its volume is ____.

If the radius and height of a cylinder are r and h respectively, then its volume is π r^{2}h

#### If the length, breadth and height of a cuboid are 24 cm, 6 cm and 5 cm respectively, then its total surface area is ____.

Given, length, l = 24 cm, Breadth, b = 6cm, Height, h = 5cm We know that, Total surface area of a cuboid = 2(lb + bh +lh) = 2(24 × 6 + 6 × 5 + 5 × 24) = 2(144 + 30 + 120) = 2 × 294 = 588 cm^{2} Hence, the total surface area of the cuboid is 588 cm^{2}

#### The number of cubes of edge 2 cm can fit in a box of volume 480 cm^{3} is ____.

Let the length of edge of the cube be a and the number of cubes be n. Given, a = 2 cm and volume of the box =480 cm^{3} ⇒n× a^{3}=480 ⇒n×8=480 ⇒n=60 Hence, the required number of cubes is 60.

#### Curved surface area of a roller is 264 m^{2} If it takes the roller 10 revolutions to level a piece of ground, area of the ground is 2640 m^{2}

Area of the ground = 10 × curved surface area of the roller = 10 × 264 =2640 m^{2} Hence, the area of the ground is 2640 m^{2}

#### If the height and radius of a right circular cylinder are 35 cm and 5 cm respectively, then the volume of the cylinder is ____.

Given, height of the cylinder, h= 35cm Radius of the cylinder, r = 5cm Volume of the cylinder, V = π r^{2}h = 22 /7 × 5 × 5 × 35 = 2750 cm^{3} ∴ The volume of the cylinder is 2750 cm^{3}

#### The breadth and height of a cuboid are 5 cm and 2 cm respectively. If the volume of the cuboid is 50 cm^{3}, then its length is ____.

Given, volume of cuboid (V) = 50 cm^{3} Height of cuboid (h) = 2 cm, Breadth of cuboid (b) = 5 cm We know that, V = lbh ⇒ 50 = l × 5 × 2 ⇒ l = 50 /10 ∴ Length of the cuboid = 5 cm