SolveItClass 10 · NCERT

NCERT Solutions · Class 10 Mathematics Surface Areas and Volumes

17 questions · 17 still being checked

EXERCISE 12.1 1–9 (part 1 of 2)

  1. Unless stated otherwise, take \(\displaystyle \pi=\frac{22}{7}\).

    Exercise 1

    2\displaystyle 2 cubes each of volume 64 cm3\displaystyle 64 \mathrm{~cm}^{3} are joined end to end. Find the surface area of the resulting cuboid.
    NCERT’s answer
    $\displaystyle 160 \mathrm{~cm}^{2}$

    Working being prepared

  2. Exercise 2

    A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14\displaystyle 14 cm and the total height of the vessel is 13\displaystyle 13 cm. Find the inner surface area of the vessel.
    NCERT’s answer
    $\displaystyle 572 \mathrm{~cm}^{2}$

    Working being prepared

  3. Exercise 3

    A toy is in the form of a cone of radius 3.5\displaystyle 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5\displaystyle 15.5 cm. Find the total surface area of the toy.
    NCERT’s answer
    $\displaystyle 214.5 \mathrm{~cm}^{2}$

    Working being prepared

  4. Exercise 4

    A cubical block of side 7\displaystyle 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.
    NCERT’s answer
    Greatest diameter = $\displaystyle 7$ cm, surface area = $\displaystyle 332.5 \mathrm{~cm}^{2}$

    Working being prepared

  5. Exercise 5

    A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter l\displaystyle l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.
    NCERT’s answer
    $\displaystyle \frac{1}{4} l^{2}(\pi+24)$

    Working being prepared

  6. Exercise 6

    A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends (see Fig. 12.10\displaystyle 12.10). The length of the entire capsule is 14\displaystyle 14 mm and the diameter of the capsule is 5\displaystyle 5 mm. Find its surface area.NCERT_Question_Class10_Maths_Ch12_Ex12-1_Q6
    NCERT’s answer
    $\displaystyle 220 \mathrm{~mm}^{2}$

    Working being prepared

  7. Exercise 7

    A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1\displaystyle 2.1 m and 4\displaystyle 4 m respectively, and the slant height of the top is 2.8\displaystyle 2.8 m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of ₹500\displaystyle 500 per m2\displaystyle \mathrm{m}^{2}. (Note that the base of the tent will not be covered with canvas.)
    NCERT’s answer
    $\displaystyle 44 \mathrm{~m}^{2}, ₹ 22000$

    Working being prepared

  8. Exercise 8

    From a solid cylinder whose height is 2.4\displaystyle 2.4 cm and diameter 1.4\displaystyle 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm2\displaystyle \mathrm{cm}^{2}.
    NCERT’s answer
    $\displaystyle 18 \mathrm{~cm}^{2}$

    Working being prepared

  9. Exercise 9

    A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in Fig. 12.11. If the height of the cylinder is 10\displaystyle 10 cm, and its base is of radius 3.5\displaystyle 3.5 cm, find the total surface area of the article.NCERT_Question_Class10_Maths_Ch12_Ex12-1_Q9
    NCERT’s answer
    $\displaystyle 374 \mathrm{~cm}^{2}$

    Working being prepared